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METHODS IN EDUCATION 



METHODS IN EDUCATION 



BY 

THOMAS J. McEVOY 




Price, $1.50 



PUBLISHED BY THE AUTHOR 

306 FULTON STREET, BROOKLYN. N. Y. 
1911 



v4' 



Covyright, 1908, 1911 
By Thomas J. McEvoy 



First edition, September, 1908 
Reprinted, May, 1911 






THE • PLIMPTON • PRESS • NORWOOD • MASS • U • S • A 



(gCI.A292240 



^ 



^ 



PREFACE 



This book is a working guide for students and teachers 
who are striving for unity in education. Content, arrange- 
ijient, and style are determined by existing needs, and the 
^ treatment as a whole conforms to modern educational 

thought. 

The first edition was announced as the cumulative 
product of contributions from pupils, students, and teachers. 
It embodied the results of experience in normal schools, 
summer schools, teachers' institutes, and the elementary 
schools of New York City. Immediate public acceptance 
was a gratifying indication of the demand for terse, prac- 
tical, and specific presentation. This second edition has the 
same characteristics, but the revision of subject-matter 
carries the benefit of three years more of experience in 
working with hundreds of graduates from the leading 
pedagogical schools of America. 

Personal gratitude is expressed for all sources of help in 
making this book a true exposition of what has been done 
and should be done in systematic education. 

New York City, May, 1911. 



9 



10 



11 



CONTENTS 

[References are to pages] 

CHAPTER I 
Introduction: The Scope of this Book 
of educa- 



The purpose 

tion 3 

Our general view or plan 3 



3. Meaning of pedagogics 

4. Scope of methods in edu- 

cation 



CHAPTER II 
The Curriculum 



5. Curriculum and course 

of study distinguished 5 

6. The teacher and the 

course of study 5 

7. The pupils and the 

course of study 5 

8. Principles determining 

course of study 6 

Butler on the course of 

study 6 

An eclectic course of 

study 7 

Contrast of courses of 

study 7 



12. 
13. 



14. 
15. 



16. 
17. 

18. 



Enriching the course of 
study 

The culture epoch 
theory in relation to 
course of study .... 

Correlation of studies . 

Report of the Commit- 
tee of Fifteen on cor- 
relation of studies . . 

Concentration of studies 

Co-ordination of studies 

Correlation, concentra- 
tion, and co-ordina- 
tion distinguished . . . 



CHAPTER III 
Maxwell on the Course of Study 



19. A modern type 

20. Principles and methods 

21. Object of education . . 

22. Harmony with environ- 

ment: intellectual . . 

23. Harmony with environ- 

ment : moral and 
ethical 

24. Harmony with environ- 

ment: physical .... 

25. Summary 

26. Extent of intellectual 

inheritance 

27. Literary inheritance . . 

28. Aesthetic inheritance . . 



15 


29 


15 


30 


16 


31 




32 


16 


33 




34 




35 


16 


36 


17 


37 


17 


38 


18 


39 


18 


40 


18 





9 
10 



11 
13 
14 



14 



Scientific inheritance . 19 

Institutional inheritance 19 

Religious inheritance . 19 

Assimilation by child . 20 

Variety 20 

Quantity of matter ... 21 

Objectivity 21 

Continuity, correlation, 

variety 22 

Objectivity 22 

Logical unity or con- 
tinuity 23 

Correlation 26 

Substitution or variety. 33 



vu 



vm 



CONTENTS 



CHAPTER IV 
Principles of Education 



41. Justification of this 

chapter 35 

42. Limitations and options 35 

43. Consciousness 36 

44. Mind 36 

45. Kno^\■ing 36 

46. Feehng 36 

47. WilUng 36 

48. WiU 36 

49. Faculties 36 

50. Object, action, product 

of a faculty 36 

51. Attention 37 

52. Interest 37 

53. Apperception 37 

54. Sensation 38 

55. Sense-perception: the 

gathering of percepts 38 

56. Observation 38 

57. Memory: storing con- 

cepts 39 

58. Imagination: building 

concepts 39 

59. Conception: holdingcon- 

cepts 39 



60. Concept 

61. Judgment: connecting 

concepts 

62. Reasoning: deriving con- 

cepts 

63. Self -activity 

64. Habit 



Training the Mind 
The plan simplified . . . 

The plan outlined 

Explanation of the plan 

Classification of Principles or 
68. Lack of agreement .... 

The principle of sense- 
perception 

The principle of motor 
reaction 

The principles of atten- 
tion and interest .... 

The principle of apper- 
ception 

The principle of self- 
activity 

Other principles 



65. 

66. 
67. 



69 



70 



71 



72. 



73. 



74. 



39 

39 

39 
39 
39 

40 
40 
40 

Laws 
41 

42 

42 

43 

43 

44 
44 



CHAPTER V 
Methods in School Econoihy 



75. Meaning 45 

76. Space 45 

77. Light 45 

78. Doors and windows ... 46 

79. Air shafts 46 

80. Indirect method 46 

81. Gra\-ity system 47 



82. Fireplace 47 

83. Seating: adjustable 

equipment 47 

84. Decoration: relation to 

school spirit 47 

85. Grounds: suggestions 

from England 48 



CHAPTER VI 
Methods in School Management 



86. Opinions 

87. Principles 

88. Definite responsibility 

89. Free discussion 



50 
50 
50 
50 



90. Spontaneity and origi- 

nality 51 

91. Qualifications of teachers 52 

92. Maxwell on marking 

teachers 52 



CONTENTS 



IX 



How to Estimate a Teacher's Value 

93. Important things in 

teaching ability .... 52 

94. Signs of poor teaching 

ability 52 

95. Personality of teacher . 53 

96. Control of class 53 

97. Suggestion 53 

98. Teaching by suggestion 54 

99. The law of habit 54 

100. The law of change or 

• variety 54 

Opening Exercises 

101. Justification 54 

102. Value of habit 55 

103. Memory gems 55 

104. Desire 56 

105. Interest in songs 56 

106. Expectancy: declama- 

tion 56 

107. Monitors 56 

108. Motives 56 

109. Anecdotes 56 

lir. The teacher an ex- 
ample 56 

111. Honor roll 56 

112. Fellowship 56 

113. Our platform 56 

114. Grading 58 

115. Promotion 58 

116. Class teaching 59 

117. Group teaching 59 

118. General use 60 

119. Adapted to each pupil 60 

120. Vigorous teaching .... 60 

121. Study periods 60 

122. Concentrated attention 60 

123. Promotion facilitated . 60 

124. No tiresome repetition 60 

125. Difficulties and advan- 

tages 61 

126. Individual teaching . . 61 

127. The Batavia plan 62 

Examinations 

128. For pupils 62 

129. Methods of conducting 

examinations 63 



130. Advantages of written 

tests 68 

131. Disadvantages of writ- 

ten tests 63 

132. Advantages of oral ex- 

aminations 63 

133. Disadvantages of oral 

examinations 63 

134. Reviews 63 

135. Home lessons 64 

136. Advantages of home 

study 64 

137. Disadvantages of home 

study 64 

Moral Education 

138. A contribution from 

New York City 65 

139. Moral aim 65 

140. Personality of teacher 65 

141. Reverence 65 

142. Self-respect 65 

143. Principle in character 66 

144. Spirit of school 66 

145. Social membership ... 66 

146. Self-government 67 

147. Moral values of studies 67 

148. Contemporary civiliza- 

tion 68 

149. Topics for moral les- 

sons • . 68 

Principles of Moral Instruction 

150. Development 69 

151. Cultivation of imagi- 

nation 69 

152. Employ self-activity . 69 

153. Positive vs. negative . . 69 

154. Supremacy of law ... 70 

155. Discipline 70 

156. Authority 70 

157. Co-operation of par- 

ents 70 

Punishment 

158. Definition 71 

159. Detention 71 

160. Assignment of extra 

tasks 72 



CONTENTS 



161. Demerit marks 72 

162. Expulsion 72 

163. Incentives 73 

164. Self-government of 

pupils 73 

165. Public opinion in 

school 74 



166. Evils 74 

167. Virtues 74 

168. Affiliated interests ... 74 

169. Adolescence 74 

170. Fatigue 75 

171. Devices in manage- 

ment 75 



CHAPTER VII 
Methods of Teaching 



172. 


Definition 


76 




173. 


Classification 


77 




174. 


Conversational method 


77 


193 


175. 


Development method . 


77 


194. 


176. 


Lecture method 


78 


195. 




Questioning 




196. 


177. 


Bases 


78 




178. 


Consecutive question- 




197. 




ine 


79 




179. 


Promiscuous question- 




198 




ing 


79 




180. 


Simultaneous question- 




199 




ing 


79 


200 


181. 


Development questions 
and review questions 




201 




distinguished 


80 


202. 


182. 


Rules 


80 




183. 


Positive rules 


80 




184. 


Negative rules 


81 




185. 


Weak questioning .... 


81 




186. 


Socratic method 


82 


203. 


187. 


Value of the Socratic 








method 


82 


204 


188. 


Irony in Socratic 




205 




method 


82 


206 


189. 


Limitations in use of 




207 




Socratic method . . . 


82 


208 


190. 


Illustration of Socratic 








questioning in 




209 




mathematics 


82 


210 


191. 


Illustration of Socratic 
questioning in gram- 




211 




mar 


84 


212 


192. 


Another illustration of 








Socratic questioning 


84 


213. 



Answers 



The kind wanted .... 85 
The educational value 

of answers 85 

Characteristics of good 

answers 85 

What answers should 

be received 85 

What answers should 

be rejected 86 

From the particular to 

the general 86 

Simple to complex ... 87 
Concrete to abstract . . 88 
From the known to the 

related unknown ... 88 
Observation before 

reasoning; processes 
before rules ; facts 
before definitions or 

principles 89 

From the empirical to 

the rational 89 

Heuristic method .... 90 

Prussian method 91 

Inductive method .... 91 
Deductive method ... 92 
The inductive-deduc- 
tive method 92 

Analytic method 93 

Synthetic method .... 93 
Comparison of analy- 
sis and synthesis ... 94 
Individual things vs. 

classes 94 

Topical method 95 



CONTENTS 



XI 



214. 
215. 

216. 

217. 



Discussion in class .... 95 

Advantages of discus- 
sion in class 95 

Dangers in discussions 
in class 96 

Directions for creating 



218. 



219. 



and profitably con- 
ducting a discus- 
sion 96 

Characteristics of effec- 
tive discussion 96 

Text-book method ... 96 



CHAPTER VIII 
General Method 



220. 


Device, method, gen- 




229. 


• 


eral method 


98 


230. 


221. 


Herbartian view of the 








order of the mind . . 


99 


231. 


222. 


Justification of the for- 








mal steps 


100 


232. 


223. 


Preparation 


100 




224. 


Presentation 


101 


233. 


225. 


Comparison or associa- 








tion 


101 




226. 


Generalization 


101 


234. 


227. 


Application or drill . . . 


101 


235. 


228. 


Aims 


102 





Rein on aim 102 

Dr. Hervey on formal 
steps of instruction 103 

Dr. Hervey's conclu- 
sion 104 

Colegrove on formal 

steps of instruction . 104 

Illustrative lesson on 
attribute comple- 
ment 105 

Method-whole 108 

Definition of method- 
whole 109 



OTAPTER IX 

_ ' Spelling 



236. Accuracy a worthy aim 110 

237. Value of spelling 110 

238. Psychology of spelling . 110 

239. The problem Ill 

Difficulties in Suhject-M alter 

240. Composite language . . Ill 

Difficulties in Pupils 

241. Not knowing how to 

study 112 

242. Failure in observation 112 

243. Carelessness 113 

Difficulties in Teachers 

244. Defective teaching ... 113 

245. Using eye alone 113 

246. Rote work 114 

247. Neglect of spelling as a 

subject 114 

248. Abuse of dictation ... 114 

249. Indistinct concepts ... 115 

250. Lapses 115 



251. Unscientific classifica- 

tion 115 

252. Interruption 115 

253. Lack of variety 115 

254. Excuses for failure ... 115 

255. What words shall pu- 

pils spell? 115 

Arguments for Text-book 

256. Convenience 116 

257. System 116 

258. Breadth and utility . . 116 

259. Accuracy 116 

260. Stimulus 116 

Arguments for Lists of Selected 
Words 

261. Specific utility 116 

262. Interest 117 

263. Adaptation 117 

264. Economy of efTort ... 117 

265. Correlation 117 

266. Summary of arguments 117 



Xll 



CONTENTS 



267. Combination of book 

and lists 117 

268. Three ways of con- 

ducting recitations . 117 

269. Advantages of oral 

spelling 118 

270. Disadvantages of oral 

spelling 118 

271. Advantages of written 

spelling 118 

272. Disadvantages of writ- 

ten spelling 118 

Directions for Studying Spelling 
Lessons 

273. Physical conditions . . 118 

274. Responsibility a stimu- 

lus 118 

275. Concentration 119 

276. Reproduction 119 

277. Comparison 119 

278. Repetition 119 

279. Rowe quoted 119 

280. Difficulties 120 

281. The old way 120 

Experiments in Studying Spelling 

282. In Germany 120 

283. Suggestions to the 

teacher 122 

284. Rules for spelling 122 

285. Classification of words 123 

286. How to teach synonyms 124 

287. How to teach homo- 

phones 129 

288. How to teach homo- 

nyms 129 

How to Teach the Meaning of Words 

289. Associative or objec- 

tive process 130 



290. By imitation 130 

291. By the context 130 

292. By etymology 131 

293. By the history of words 132 

294. By finding synonyms . 132 

295. How pupils may show 

their knowledge of 

the meaning of words 133 

296. Means of learning pro- 

nunciation 133 

297. Uses of the dictionary 133 

298. Devices in word-build- 

ing 133 

299. Grouping words by 

comparison 134 

300. Grouping by contrast . 135 

301. Correlation through 

dictation 135 

302. "Make every lesson a 

spelling lesson" .... 136 

303. Pronunciation of each 

syllable 136 

304. Repetition in writing 

misspelled words . . . 136 

305. Combination plan .... 136 

306. Self-correction 136 

307. Interchange 137 

308. Monitor 137 

309. Group criticism 137 

310. Individual responsi- 

bility 137 

311. Class responsibility .. . 138 

312. Alertness 138 

313. Choosing sides 138 

314. Spelling down 138 

315. Pupils as examiners . . 138 

316. Pupils as reviewers . . . 138 

317. Pupils as critics 138 

318. Pupils as friends 139 



CHAPTER X 
Composition 



319. Utility and culture ... 140 

320. General aims 140 

321. The pupils' motives: 

pleasure, sponta- 
neity, interest 141 



322. Principles determining 

selection of matter 

for compositions . . . 141 

323. Suggestions for the 

teacher 142 



CONTENTS 



Xlll 



324. 

325. 

326. 
327. 

328. 
329. 

330. 
331. 
33S. 
333. 
334. 
335. 
336. 

337. 

338. 
339. 
340. 

341. 

342. 
343. 
344. 
345. 
346. 
347. 



374. 

375. 
376. 
377. 

378. 
379. 

380. 



381. 
382. 



Kinds of composition 

exercises 143 

Oral composition .... 143 

In primary grades .... 143 
Dr. Maxwell on oral 

composition 143 

Optional classification. 144 
Transcription or copy- 
ing 144 

Dictation 145 

Forms of expressions . . 145 

Reproduction 145 

Paraphrase 145 

Abstract 146 

Elaboration 146 

Kinds of written com- 
position 146 

Problems 146 

Selection of subjects . . 146 
Some suitable subjects 147 
The model as a prepa- 
ration for writing . . 148 
The selection of a 

model 148 

The study of the model 148 

Imitation of the model 149 

The model in criticism 150 

Outlines 150 

Purposes of outlines . . 150 
Composition without 

model 150 



348. Criticism of composi- 

tions 151 

349. Suggestions on criti- 

cisms 151 

350. Too many rules 152 

351. The sentence 152 

352. The paragraph 153 

Pertinent Questions Answered 

353. Rewriting composi- 

tions 153 

354. Occasional rewriting . . 153 

355. Original drafts 154 

356. Ink or pencil 154 

357. Envelopes 154 

358. Consulting references . 154 

359. Choice of model 154 

360. Cause of errors 154 

361. Time before criticism . 154 

362. Effect of criticism .... 155 

363. No criticism 155 

364. Signature of -critic ... . 155 

365. Coloried pencil used . . 155 

366. Errors indicated .... 155 

367. Self-correction 155 

368. Time limits 155 

369. Pupils choose subjects. 156 

370. Reading best work ... 156 

371. Writing poetry 156 

372. General progress .... 156 

373. Question answered . . 156 



CHAPTER XI 

Grammar 



Value of technical 

grammar 159 

Scope of this chapter . 160 
A habit of thinking . . 160 
Facts before conclu- 
sions 100 

The syllogism 161 

Fundamental facts in 

grammar 161 

Development based 
upon fundamental 

facts 162 

Types 164 

Independent elements. 164 



383. Simple sentence first . 164 

384. Maxims applied .... 164 

385. Content of illustrative 

sentences 164 

386. Oral analj'sis 165 

387. Diagrams 165 

388. Drill 166 

389. Parsing literary mas- 

terpieces 167 

390. False syntax 168 

'391. Types of lessons .... 169 

392. Parts of speech 169 

393. Development lesson on 

the noun 170 



XIV 



CONTENTS 



394. Development, lesson on 

attribute complement 171 

395. Predicate, adjective, 

and adverb modifiers 
distinguished 171 

396. Personal pronoun and 

relative pronoun .... 173 

Shall and Will 

397. Meaning and us 174 

398. Rule 175 

399. Rule 175 

400. Rule 175 

Should and Would 

401. Applications 176 

402. Modes 176 

403. Drill on Modes 177 

Participles and Infinitives 

404. The meaning of terms 

used 178 

Participles 

405. Lesson on participle 

used as an adjective . 179 

406. Uses of participles ... 181 

407. Distinctions required . 181 

408. Drill on participle used 

as adjective; verbal, 

or verbal adjective . 183 

409. Drill on participles used 

as nouns; gerunds, 

or verbal nouns .... 184 



410. Drill on participle used 

as a mere adjective . 184 

411. Drill on participle used 

as a mere noun .... 185 

Infinitives 

412. Uses of infinitives .... 186 

413. Drill on infinitives used 

as nouns 186 

414. Drill on infinitives used 

as adjectives 187 

415. Drill on infinitives used 

as adverbs 187 

416. The infinitive without 

to 187 

417. Words, phrases, clauses 188 

418. Drill on adjective 

clauses 189 

419. Development: Con- 

cord of relative pro- 
noun and antecedent 190 

420. Development: The 

noun clause 191 

421. Drill on noun clauses . 193 

422. Connectives: Explana- 

tion and drill 194 

423. Distinctive uses of con- 

nectives illustrated . 197 

424. Synthetic drill on con- 

nectives 197 

425. Assignment 198 

426. Exercises in false syn- 

tax 198 



CHAPTER XII 
Geography 



427. The old and the new . . 201 

428. The old way 201 

429. The new way 202 

430. Definitions of geog- 

raphy 202 

431. Broader educational 

use 203 

432. The courses of study . 203 

433. Introductory note . . . 203 

434. Practical purposes . . . 204 

435. Intellectual purposes . 205 

436. Ethical purposes 206 



437. Col. Parker quoted . . 207 

438. Home geography .... 208 

439. Fundamental facts ... 208 

440. Early lessons 208 

441. Points of compass .... 209 

442. Distance 209 

443. Maps 209 

444. Models 210 

445. Constructive imagina- 

tion 211 

446. Analytic and synthetic 

methods 211 



CONTENTS 



XV 



447. Synthetic method 212 

448. Both methods com- 

bined 212 

449. Excursions 213 

450. McMurry on excur- 

sions 214 

Committee of Ten Quoted 

451. Order of treatment . . , 214 

452. Representative geog- 

raphy 214 

453." Derivative or descrip- 
tive geography .... 215 

454. Rational geography . . 215 

455. Observational geog- 

raphy 216 

456. Concentric circles .... 217 

457. Illustration of concen- 

tric arrangement . . 218 

458. Causal relations 219 

459. Causal series 219 

460. Man and nature 219 

461. Types in geography. . . 221 

462. Home city a type 222 

463. Comparison 224 

How to Study 

464. A plan suggested .... 225 

465. Continents as wholes . 225 

466. Plan for studying a 

country 225 

467. The recitation 226 

468. Use of pictures 227 

469. OutHnes by pupils ... 228 

470. Aids 228 

471. Dr. Maxwell on geog- 

raphy 228 

472. Suggestions to princi- 

pals 228 

473. Results that are essen- 

tial 229 

Suggestions for Devices 

474. Concrete aids 229 

475. Outline maps 229 

476. Product maps 230 

477. Scrap-book 230 



478. Pupils as examiners . . . 230 

479. Class discussion 230 

480. Debates 231 

481. Commercial trips .... 231 

482. Geographical cards ... 231 

483. Competition 231 

484. The globe an essential . 232 

485. Uses of the globe 232 

486. The shape of the earth 233 

Climate 

487. Extension of the term . 235 

488. Conditions affecting 

climate 236 

489. Forms of moisture .... 237 

490. Rain 238 

491. Glaciers 240 

492. Icebergs 242 

493. The seasons 242 

494. Zones 244 

495. Isotherms . . .* 244 

Latitude and Longitude 

496. A lesson outlined 245 

497. International date line. 247 

498. Standard time 248 

499. Volcanoes: concrete 

presentation 248 

500. Winds 250 

501. Trade winds 251 

How to Study a Map 

502. Importance 252 

503. The process of studying 

a map 253 

How to Study the Text 

504. Difficulties 254 

505. The process of study- 

ing the text 255 

506. Suggestions for the aid 

of pupils in studying 

the text 255 

507. Characteristics of mod- 

ern text-books 256 



XVI 



CONTENTS 



CHAPTER XIII 
History and Civics 



508. An institutional sub- 

ject 257 

509. Early work in history . 257 

510. Geographical back- 

ground 257 

511. Current events, anni- 

versaries, excursions 258 



512. 
513. 

514. 

515. 

516. 

517. 
518. 

519. 
520. 

521. 
522. 
523. 

524. 

525. 

526. 



Civics 



258 



Members of society. 

Topics for discussion in 

all grades 258 

Importance of local or- 
dinances 259 

Government by the 
people 259 

Aim of history and 

civics 259 

Result sought 260 

Habituation to civic 

requirements 260 

Definition of history . . 260 

Value of the study of 

history 261 

The historical sense . . 262 

Extent of history .... 261 

Method of teaching 
history 263 

Method in the lower 
grades 263 

The teacher's prepara- 
tion 264 

Topical method 266 



527. Text-book method . . 267 

528. Source method 267 

529. Collateral reading .... 268 

530. Open text-book recita- 

tion 269 

531. Cause and effect 269 

532. What should be memo- 

rized? 270 

533. Verbal repetition .... 270 

534. Correlation 271 

535. Reviews 271 

536. Use of outlines 273 

537. Note books 273 

538. The use of maps 273 

539. Progress maps 274 

540. Debates 274 

541. Questions prepared by 

pupils 274 

542. The use of illustrations 275 

543. Collection of prints and 

pictures 275 

544. Excursions 275 

545. Dramatization of his- 

toric events 275 

546. Use of mnemonics .... 276 

547. How to arouse interest 276 

548. Civics 276 

549. Local government .... 276 

550. Process of legislation . 277 

551. Institutional study of 

history and civics . . 277 

552. Common mistakes in 

teaching history and 

civics 277 



CHAPTER XIV 

Reading 



553. Value 279 

554. Characteristics of books 

formerly used 279 

555. Complete works vs. 

selections 280 

556. Guiding principle to- 

day 281 



557. 



558. 



559. 
560. 



Types of reading mat- 
ter used at present . 281 

Principles determining 
the selection of read- 
ing matter 282 

Analytic method .... 282 

Word method 282 



CONTENTS 



xvii 



561. Sentence method .... 283 

562. Meaning of synthetic 

method 283 

563. Alphabet method 283 

564. Phonic method 284 

565. Advantages of phonic 

training 284 

Analytic-Synthetic Methods 

566. Distinction not ac- 

. cepted 284 

567. Combination method . 285 

568. Dramatization 285 

569. Arguments for drama- 

tization 286 

570. Features 287 

Ward Method 

571. Self-help 289 

572. Sight reading and drill 289 

573. Features 289 

Aldine Method 

574. A general outline .... 290 

575. The method justified . 291 

576. Summary of advan- 

tages claimed 294 

McCloskey and Aldine Combined 



577. Eclectic tendency . . . 

578. Good reading defined 

579. Physical difficulties . 

580. Mental difficulties . . 

581. Reading to pupils . , . 

582. Meaning of words . . . 



294 
296 
296 
296 
297 
297 



How to Arouse Interest in Reading 

583. Information and drill . 297 

584. Removing difficulties . 298 

585. Enlarging native inter- 

ests 299 

586. Appreciative reading . 299 

587. Oral reports 300 

588. Memorizing 300 



589. Silent reading . . .• 300 

590. Violations of articula- 

tion 301 

591. Definitions of accent 

and Cimphasis 301 

592. Emphasis illustrated . 301 

593. Meaning and kinds of 

inflection 302 

594. Monotone 302 

595. Rising inflection 302 

596. Falling inflection .... 303 

597. Circumflex for under- 

scored words 303 

598. Kinds of modulation: 

pitch, quantity, 

quality 303 

599. Meaning of quality of 

tone 304 

600. Pure tone 304 

601. Orotund 304 

602. Aspirated tone 305 

603. Guttural quality 305 

604. Grammatical and rhe- 

torical pauses 305 

605. Control of the breath . 306 

606. Extensive and inten- 

sive reading 306 

607. Home reading 307 

608. Literature and char- 

acter 307 

609. Patriotic selections . . . 308 

610. Biography 308 

How to Memorize a Selection 

611. The selection 308 

612. Copy in sight 309 

613. Biography of author . 309 

614. Occasion of writing . . . 309 

615. Business-like attack . . 309 

616. Physical comfort 309 

617. The memorizing 309 

618. Unifying review 309 

619. Rhetorical exercises . . 310 

620. Adaptation 310 

621. Variety 310 

622. Correlation 310 

623. Memory gems: limi- 

tations 311 



XVlll 



CONTENTS 



CHAPTER XV 

Akithmetic 



624. 

625. 

626. 
627. 

628. 
629. 
630. 

631. 
632. 



633. 



634. 



635. 



Changing points of 

view 316 

Quantity, measure- 
ment, mathematics 316 
Definition of number . 316 
Counting and measur- 
ing 320 

Arithmetic and its aim 321 
Utility of arithmetic . . 322 
Important historical 

facts 323 

Method in arithmetic . 325 
Methods of teaching 
the concept of num- 
ber 327 

Concrete number oper- 
ations, order of suc- 
cession 328 

Summary of modes of 
concrete number 

operations 329 

The use of a book by 
pupils 330 



Devices for Drill in Primary Grades 

636. A distinction repeated 330 

637. Cards 331 

638. Charts 331 

639. Mimeograph work ... 331 

640. Text-books 331 

641. Board 331 

642. Circle 331 

643. Square 331 

644. Drawing 331 

645. Dictation 331 

646. Competition 332 

647. Decimation 332 

648. How to mark papers . . 332 

649. The nature of the prob- 

lems 333 

650. Opinions on drill 334 

651. The fundamental oper- 

ation 334 

652. Hint from experience 

of the race 334 



Addition 

653. A kind of counting . . 335 

654. The forty-five combi- 

nations 336 

655. Automatic habits .... 336 

656. Two fundamental facts 337 

657. Decomposition 337 

658. Algorisms 338 

659. Laws or principles of 

addition 339 

Subtraction 

660. Relation to addition . . 339 

661. Decomposition to ex- 

plain borrowing . . . 339 

662. Equal additions to ex- 

plain borrowing . . . 340 

663. Complementary addi- 

tion in subtraction . 340 

664. Four ways of perform- 

ing subtraction .... 341 

665. Principles of subtrac- 

tion 341 

666. Proof of subtraction . . 342 

Multiplication 

667. Special case of addition 342 

668. Counting 342 

669. Decomposition 342 

670. Justification 343 

671. Multiplication by fac- 

tors 344 

672. Justification by com- 

mutative law 344 

673. Commutation, associa- 

tion, distribution . . 344 

674. Multiplication tables: 

mode and order of 
learning 345 

675. Principles of multipli- 

cation 346 

676. Proof of multipHcation 346 

677. Concrete and abstract 

numbers in multipli- 
cation . . . . ^ 346 



CONTENTS 



XIX 



Division 

678. Nature of division .... 347 

679. Measurement and par- 

tition 347 

680. Short division; long 

division 348 

681. Division by factors 

(associative law) . . . 349 

682. Laws or principles of 

division 349 

683. Proof of division 349 

6SJ:. Grube method: char- 
acteristics, advan- 
tages 349 

685. Objections to the 

Grube method 349 

686. Speer method 350 

687. Graphic methods .... 350 

Properties of Number for Primary 
Grades 

688. Extent of work 351 

689. Odd and even 351 

690. Prime and composite . 351 

691. Divisibility 352 

Properties of Number for Higher 

Grades 

692. Induction and deduc- 

tion 

693. Commutative, associa- 

tive, and distributive 
laws 

694. Other general proper- 

ties 

695. References 

696. Application: tests of 

divisibility 353 

697. Types of demonstra- 

tion 354 

698. Test by 3 354 

699. Frequent use of syllo- 

gism 355 

700. Common divisors and 

factors; highest 
common factor .... 356 

701. By observation 357 

702. By product of prime 

factors 357 

703. By continued division . 358 



352 



352 

352 
353 



704. Definitions of multiples 360 

705. First method 360 

706. By multiplying prime 

factors 360 

707. Factoring by inspec- 

tion 361 

708. Actual division 361 

709. ByaidofG. C. D 361 

Fractions 

710. Common fractions . . . 362 

711. Principles or laws of 

fractions 363 

712. Three conceptions of 

fractions 364 

713. Changing to equivalent 

fractions 365 

714. Reduction to lowest 

terms 366 

715. Whole or mixed num- 

bers 366 

716. Addition 366 

717. Subtraction 366 

718. Multiphcation 366 

719. Multiphcation: frac- 

tion by fraction. . . . 367 

720. Faulty arrangement. . . 369 

721. Division: fraction by 

integer 369 

722. Division: fraction by 

a fraction 370 

723. Equation introduced . 372 

724. Division: integer by 

fraction 372 

Decimal Fractions 

725. Relation to common 

fractions 372 

726. Suggestions of early 

lessons 373 

727. The decimal point 373 

728. Principles 374 

729. Development lesson: 

notation and nu- 
meration 374 

730. Addition and subtrac- 

tion 375 

731. Division: related to 

common fractions . . 377 



XX 



CONTENTS 



732. Division: Austrian 

method 377 

733. Division: inverse of 

abbreviated multi- 
plication 378 

Denominate Numbers 

734. Turn to use 379 

Percentage 

735. Relation to fractions . . 380 

736. Method of common 

fractions 380 

737. Method of decimal 

fractions 381 

738. The method of the 

equation 381 

Simple Interest 

739. Terms used 383 

740. Methods 383 

741. Faulty arrangement . . 383 

Miscellaneous Topics 

742. Algebra used in arith- 

metic 384 

743. Ratio 384 

744. Short process and busi- 

ness methods 384 

745. Unitary analysis 386 

746. Variable unit 386 

747. Series 386 

748. Arithmetical comple- 

ment 387 

749. Problems 387 

750. Proof, verification, or 

checking 387 

751. Rule 387 

Text-Books in Arithmetic 

752. Guiding principles 388 

753. Elimination of subject- 

matter 389 

754. Content of the prob- 

lems 390 

755. Types of books 390 



New York City Point of View 

756. Suggestions 392 

757. General directions . . . 392 

758. The combinations .... 392 

759. Addition and miilti- 

plication 393 

760. Subtraction and di- 

vision 394 

761. Constructive " and in- 

ventional exercises . 394 

762. Problems 395 

763. What to look for in the 

solution of problems 395 

764. Analysis in solution . . 395 

765. Rote work criticised . . 395 

766. Progressive advance in 

difficulties by grades 396 

767. Problems illustrating 

progressive order of 

difficulties 399 

768. Methods applied in 

New York City 401 

Addition 

769. Grade lA 401 

770. Grade IB 402 

771. Grade 2A 403 

772. Grade 3A 404 

Subtraction 

773. Grade lA 404 

774. Grade IB 404 

775. Grade 2A 405 

776. Grade 2B 405 

777. Grade 3A 408 

Multiplication 

778. Grade 2B 408 

779. Grade 3A 410 

780. Grade 3B 410 

Division 

781. Grade 2B 412 

782. Grade 3A 413 

783. Grade 3B 413 



CHAPTER XVI 

Questions on the Text, page 417 

Index 427 



METHODS IN EDUCATION 



METHODS IN EDUCATION 

CHAPTER I 
INTRODUCTION: THE SCOPE OF THIS BOOK 

1. The purpose of education. — It is not necessary to 
try to construct a new definition of education. By 
examining a few of the definitions we find that the best 
modern thinkers consider that education should give 
to each individual a full development of all his powers. 
This means physical power, intellectual power, and moral 
power. It is a threefold harmonious development that 
enables each individual to know, feel, and do his duty to 
himself and to the civilized community in which he 
lives. This meaning of education implies culture, 
eflficiency, discipline, knowledge, development, charac- 
ter, and citizenship, — the seven ideals found in the 
history of education in western civilization. 

2. Our general view or plan. — The purpose of edu- 
cation expresses an aim or ideal. It gives us a criterion 
for educative effort. The second desirable considera- 
tion is the subject-matter suitable in attaining the ideal, 
a consideration relating to the curriculum or course of 
study. The use of the course of study brings up the 
consideration of procedure or methods. As we take 
these considerations one by one or together, we must 
think of the child or the one to be educated. This fourth 
topic necessitates the application of psychological prin- 
ciples of education in justifying methods of teaching. 

3 



4 METHODS IN EDUCATION 

Thus a serviceable comprehension of methods in educa- 
tion impHes a blending of these five considerations: 

1. Ideals, aims or purpose in education. 

2. Subject-matter in education: the curriculum. 

3. The mind to be educated: psychology. 

4. Method in education: the processes.' 

5. General organization: school management and 
discipline. 

3. Meaning of pedagogics. — As an illustration of the 
tendency toward comprehensive treatment of topics in 
education, many schools are classifying their educational 
courses under the term pedagogics. The word peda- 
gogics is derived from two Greek words meaning the 
training or guiding of boys. Its larger signification at 
present covers the theory and the practice of teaching 
as a profession, embracing the application of history and 
principles of education, methods of teaching, school 
management, psychology, and ethics. 

4. Scope of methods in education. — The treatment of 
methods of teaching is usually restricted to particular 
ways of presenting arithmetic, geography, grammar, and 
other subjects in the curriculum. But the larger con- 
ception in modern educational thought requires the 
teacher to see and feel that the presentation of daily 
lessons is only one methodical act in habit-formation; 
all the other educative acts in and out of school are sub- 
ject to the laws governing methods of teaching. This 
book aims, therefore, as outlined in section 2, to treat 
under methods in education many aspects of school 
work not usually discussed under methods of teaching. 
This view is defended on the ground that education is 
a unified or blended result rather than an aggregate 
of a series of independent acts. 



CHAPTER II 
THE CURRICULUM 

§. Curriculum and course of study distinguished. — 

By many writers these terms are considered interchange- 
able, but the following quotation gives a good distinction: 
''By the curriculum is meant the logical, complete, and 
unified conception of the studies and exercises of the 
schools regardless of their administration, while by the 
course of study is meant the arrangement and grouping 
of these studies and exercises for the purpose of bringing 
them effectively to the learners." For an elaboration 
of this conception, see Ruediger's The Principles of 
Education, page 225. 

6. The teacher and the course of study. — The 
average teacher has little to do in making a course of 
study, but every teacher has much to do in carrying out 
the requirements of prescribed courses. It is necessary, 
therefore, to know the underlying principles so that the 
mutual rights of the child and the curriculum may be 
wisely adjusted. 

7. The pupils and the course of study. — In the first 
place, a course of study is not a rigid standard of work, 
irrespective of pupils, teacher, and methods; it is, on the 
other hand, conditioned by those three factors, and all 
four must yield to satisfy the needs of each. When 
Rousseau insisted upon a curriculum of natural material, 
adapted to the nature of the child, he directed attention 

5 



6 METHODS IN EDUCATION 

to what has recently been recognized, namely, that 
the needs of the child must determine the course of study, 
and not vice versa. 

8. Principles determining course of study. — Our 
conception of education embodies' the. reciprocal rela- 
tions of the individual and society. It is not enough 
to know our civic duties; right thinking must pass into 
right action. So the first principle is a sociological one; 
the second, psychological. The former shows what 
subject-matter will tend to develop broad, useful, effi- 
cient knowledge; the latter indicates the manner of 
adapting the chosen subjects to the capacities of indi- 
vidual minds. 

9. Butler on the course of study. — An application 
of the principles mentioned in section 8 is found in the 
course of study outlined by President Butler of Columbia 
University. In defining education he says: ''What 
does the term mean? I answer, it must mean a gradual 
adjustment to the spiritual possessions of the race. 
Those possessions are at least five-fold. The child is 
entitled to his scientific inheritance, to his literary 
inheritance, to his aesthetic inheritance, to his insti- 
tutional inheritance and to his religious inheritance." 

The scientific inheritance is found in geography, 
nature study, mathematics, and physics; the literary 
inheritance includes all forms of literary composition 
and interpretation; the aesthetic inheritance includes 
drawing, music, and all other kinds of art that may aid 
in forming a higher conception of life; the institutional 
inheritance is found in all kinds of civic training, includ- 
ing political geography, history, civics, and all the sub- 
ordinate forms of government represented in state and 
municipal organizations; and the religious inheritance 



THE CURRICULUM 7 

includes all forms of training that are conducive to 
spiritual perfection. 

The course of study in New York City is in agreement 
with the requirements mentioned by Butler. 

10. An eclectic course of study. — Modern courses 
of study are said to be eclectic because they embody 
the chosen culture products of civilization. To complete 
the. five inheritances mentioned in the last section, it 
is suggested that a sixth, industrial inheritance, be added 
to satisfy the recognition of industrial training as a part 
of systematic education. As an interesting study in 
development, recall what was taught in the oriental 
nations and then trace the history of courses of study. 
The following courses are suggested, with references 
to McEvoy's Epitome of History and Principles of 
Education: 

1. Greece — Music and Gymnastics, pages 38 and 
58. 

2. Rome — Utilitarian Tendencies, pages 60 and 70. 

3. Monasticism — Seven Liberal Arts, page 86. 

4. Early Christian Universities — Law, Medicine, 
Philosophy, Theology, page 102. 

5. Sturm — Classical High School Course, page 128. 

6. Jesuits — Ratio Studiorum, page 130. 

7. Comenius — Nature, page 154. 

8. Spencer — Science, page 216. 

9. Modern — Eclectic. See opinions of Harris, 
Dewey, DeGarmo, Butler, and others. 

11. Contrast of courses of study. — Twenty-five 
years ago the elementary school taught reading, writing, 
spelling, grammar, geography, United States history, 
and what was called civics. In order to fill in the time 
arithmetical rules of no possible use in life were taught 



8 METHODS IN EDUCATION 

and the children's wits were exercised or blunted by out- 
landish mathematical puzzles; a manual of United States 
history and the constitution of the United States were 
learned by heart; long lists of meaningless names were 
memorized in geography; parsing, with the utmost de- 
tail, was continuous; drawing, where drawing was taught, 
was exclusively from flat copies, and the crowning glory 
of the school was held to be the ability to spell sesqui- 
pedalian words whose signification had never dawned 
upon the childish intellect. 

The additions are nature study, intended to train what 
President Ehot calls the '^ capacities for productiveness 
and enjoyment" through the progressive acquisition of 
an elementary knowledge of the outside world; algebra, 
chiefly as an aid, through the equation, to the solution 
of arithmetical problems; inventional geometry; litera- 
ture, studied as such, distinct from the ordinary reading 
lesson; language and composition, as the act of expres- 
sion; drawing from objects; and manual training and 
other physical exercises. This seems a long list, and yet 
every subject is justified and required by the fundamen- 
tal assumption that the school exists for the progressive 
adaptation of the child's mind to its spiritual environ- 
ment. In other words, each child has a right to the 
acquisition not only of the tools of knowledge, but at 
least to the beginnings of a knowledge of literature, of 
science, of art, of institutions, and of ethics, so that when 
he leaves school he may be able to continue along the 
road on which he has started. — W. H. Maxwell, 
N. E. A. Address, St. Louis, 1904. 

12. Enriching the course of study. — This expres- 
sion is an indication of an effort to frame a curriculum 
that will satisfy the majority of pupils. The first para- 



THE CURRICULUM 9 

graph in section 11 mentions a rigid course formerly 
used; but as a large number of pupils must leave school 
before completing the elementary course, it is desirable 
to give them some knowledge of the advanced subjects 
which bear directly upon the affairs of life. It has been 
found, too, that for all pupils the elements of advanced 
subjects may be taught long before technical words are 
understood. This effort to give breadth, utility, and 
interest to all elementary work is called enriching the 
course of study. For illustration see second paragraph 
in section 11. 

13. The culture epoch theory in relation to course 
of study. — This theory may be expressed in these 
words: **The individual mind in its development 
repeats the order of development of the race mind." 
The history of civilization presents certain stages or 
epochs as the pastoral epoch, the nomadic epoch, the 
stone age, the bronze age, the hunting stage, the agri- 
cultural epoch, and so on. It is believed that each stage 
of race development shows certain culture products 
in rehgion, history, Hterature, etc., and that such 
culture products should be arranged in the course of 
study for the corresponding epochs or stages in child 
development. 

Opinion hy Roark 

Any attempt to apply the theory closely must be futile, 
for only the most general correspondence can be found 
between the periods of the child's development and the 
epochs of race growth. Even if it were possible to 
estabhsh exact correspondence, it would be unwise to 
plan a course of study and methods of teaching in strict 
conformity therewith, for the sufficient reason that, in 



10 METHODS IN EDUCATION 

his recapitulation, the average child exhibits some char- 
acteristics it is highly desirable to eliminate. The 
child, as the heir of the race, should be put in posses- 
sion of only the best which the race has gained for him. 
And he should be trained to adapt himself to the actual 
conditions of modern life, not to those of bygone eras. — 
Economy in Education, page 211. 

The American View 

In America this theory has not been generally ac- 
cepted. The experiments that have been made here 
are based upon the manumental arts in recognition of 
the efforts of the race to adjust itself to its material 
environments. We do, however, admit that there 
should be an adaptation of subject-matter in a course 
of study, and the culture epoch theory has given some 
aid in making this adaptation. We may broadly clas- 
sify the elementary period of school life under the imag- 
inative stage, the memory stage, and the reasoning 
stage. The general divisions of subject-matter are in 
harmony with these phases of mental activity. The 
following quotation aptly expresses the thought: '' Fairy- 
tales for the child, history for the youth, philosophy 
for the man." 

14. Correlation of studies. — Correlation is putting 
such subjects side by side at a given time in the course 
as will help to bring to view the universal relations 
involved in the study of any one of them. — Tompkins, 
Philosophy of Teaching, page 263. 

Correlation Illustrated 

" In treating the Hudson river as a type we come upon 
the mountains, forests, water power, and manufactur- 



THE CURRICULUM 11 

ing of its upper course; the navigation, cities, railroads, 
and scenery of its lower course; its commercial connec- 
tions by canal with the coal fields of Pennsylvania, with 
the forests of the north by canal to Lake Champlain, 
with the Great Lakes by the Erie canal along the 
Mohawk to Buffalo. The harbor and city of New York 
and their easy connections with the Great Lakes and the 
upper Mississippi Valley, are on one side, with the 
Atlantic coast and the marts of Europe on the other. 
Historically, the Hudson is very attractive; Hudson and 
his contact with the Indians, Washington and his cam- 
paigns, the old forts and the battle scenes, Arnold and 
Andre, Burgoyne's invasion. In Uterature Irving has 
made certain spots on its banks as famous as the old 
battle grounds. From a purely scientific standpoint, 
the great drowned valley, its palisades, mountains, and 
incoming ocean tides are at once suggested. Thus we 
have the relations of geography to history, literature, 
and natural science." 

15. Report of the Committee of Fifteen on correla- 
tion of studies. — Your Committee understands by 
correlation of studies : 

I. Logical order of topics and branches 

First, the arrangement of topics in proper sequence 
in the course of study, in such a manner that each branch 
develops in an order suited to the natural and easy prog- 
ress of the child, and so that each step is taken at the 
proper time to help his advance to the next step in the 
same branch, or to the next steps in other related 
branches of the course of study. 



12 METHODS IN EDUCATION 

II. Symmetrical whole of studies in the world of human 

learning 

Second, the adjustment of the branches of study in 
such a manner that the whole course at any given time 
represents all the great divisions of human learning, as 
far as is possible at the stage of maturity at which the 
pupil has arrived, and that each allied group of studies 
is represented by some one of its branches best adapted 
for the epoch in question; it .being implied that there 
is an equivalence of studies to a greater or less degree 
within each group, and that each branch of human 
learning should be represented by some equivalent 
study; so that, while no great division is left unrepre- 
sented, no group shall have superfluous representatives 
and thereby debar other groups from a proper repre- 
sentation. 

III. Psychological symmetry — the whole mind 

Third, the selection and arrangement of the branches 
and topics within each branch considered psycholog- 
ically with a view to afford the best exercises of the fac- 
ulties of the mind, and to secure the unfolding of those 
faculties in their natural order, so that no one faculty 
is so overcultivated or so neglected as to produce 
abnormal or one-sided mental development. 

IV. Correlation of pupiVs course of study with the world 
in which he lives — his spiritual and natural en- 
vironment 

Fourth and chiefly, your Committee understands by 
correlation of studies the selection and arrangement in 
orderly sequence of such objects of study as shall give 



THE CURRICULUM 13 

the child an insight into the world that he lives in, and 
a command over its resources such as is obtained by a 
helpful co-operation with one's fellows. In a word, 
the chief consideration to which all others are to be sub- 
ordinated, in the opinion of your Committee, is this 
requirement of the civilization into which the child is 
born, as determining not only what he shall study in 
school, but what habits and customs he shall be taught 
in the family before the school age arrives; as well as 
that he shall acquire a skilled acquaintance with some 
one of a definite series of trades, professions, or voca- 
tions in the years that follow school; and, furthermore, 
that this question of the relation of the pupil to his 
civiUzation determines what political duties he shall 
assume and what religious faith or spiritual aspirations 
shall be adopted for the conduct of his hfe. — Pages 
40, 41. 

16. Concentration of studies. — A curriculum based 
upon concentration of studies has one study as the 
centre or core, and other related studies are grouped 
around the core. Ziller, a disciple of Herbart, used 
Uterature and history as the core; Colonel Parker used 
geography; and John Dewey advocates manual training. 

Concentration favors a strict interpretation of the 
culture epoch theory. Germany favors concentration, 
but America does not. Ziller used Robinson Crusoe as 
the central study. All language lessons were based 
upon it; arithmetic measured the voyage, the time on 
the island, the number of sheep and goats, etc.; geog- 
raphy became vivid by tracing the routes and locating 
the island*; constructive powers were exercised in imitat- 
ing Robinson in making ladders, fish-hooks, tools, and 
other equipments; moral lessons were learned from Rob- 



14 METHODS IN EDUCATION 

inson's patience, kindness, and perseverance. In Amer- 
ica, Hiawatha has been used in making similar typical 
lessons. 

17. Co-ordination of studies, -r- The arrangement of 
studies in groups of equal rank is co-ordination of studies. 
See Butler's views in section 9. 

18. Correlation, concentration, and co-ordination dis- 
tinguished. — Observe that concentration makes use of 
one central study with radiating lines of related knowl- 
edge; that co-ordination makes use of more than one 
study, — five in the scheme of Harris, such groups 
being of equal value; and that correlation utilizes the 
general lines of related knowledge running through and 
unifying all the subjects and all the groups of subjects 
in the course of study. Correlation is a general term 
including concentration and co-ordination. 



CHAPTER III 
MAXWELL ON THE COURSE OF STUDY 

1^. A modem type. — The New York City Course 
of Study has been widely discussed as an illustration 
of recent efforts in the organization of subject-matter. 
Theoretically, it is ideal for a typical American city 
like New York; practically, it is requiring modification 
especially on the quantitative side. Such changes are 
expected, however good the course of study may be, on 
account of the varying needs of the community and the 
changing viewpoints in education. 

This chapter deserves consideration by students who 
desire to have a practical discussion of a course of study 
as a whole. Principles and methods are clearly exempli- 
fied in this address, which was delivered by Dr. William 
H. Maxwell, City Superintendent of Schools, before the 
New York City Teachers' Association and the Society 
for the Study of Practical School Problems. 'His sub- 
ject was Some Phases of the New Course of Study. 
The address was reported by E. F. Smith and printed 
in the Metropolitan Teacher in May, 1904. The pub- 
lishers of that magazine gave us permission to publish 
the address. 

The Address by Dr. Maxwell 

20. Principles and methods. — In discussing some 
phases of the new course of study, I shall deal princi- 

15 



16 METHODS IN EDUCATION 

pally with the foundation, the principles of education 
that seem to underlie it, and I shall take occasion inci- 
dentally to illustrate some of my points by referring to 
methods of teaching. 

21. Object of education. — The first thing to be con- 
sidered in making a course of study is that exceedingly 
difficult and exceedingly complex, but always extremely 
interesting question. What is the object of educating 
the child at all? In looking for this object, in trying 
to determine the aim of elementary school education or 
of any education, there is nothing better to be found 
than that very comprehensive statement which appears 
in the report of the Committee of Fifteen, namely, that 
the object of education is to bring the child into har- 
mony with his environment. Now what does this ex- 
pression mean? What is meant by saying that the child 
is to be brought into harmony with his environment? 

22. Harmony with environment : intellectual. — 
First, it means that in so far as our time, our ability, and 
his aptitude will permit, the child is to be put into pos- 
session of the intellectual inheritance of the race. He 
belongs to the human race, whose history has been that 
of many -great achievements, and therefore it must be 
assumed that education involves a knowledge of some of 
the things by which the race has made progress in the 
past. Some of the things, because the range of human 
knowledge is now so enormous that no one human mind 
can compass it. There are, however, certain of these 
things that any one of ordinary intelligence can compre- 
hend, can take in, and these the child should compre- 
hend if he is to be in harmony with his environment. 

23. Harmony with environment: moral and eth- 
ical. — Second, the bringing of a child into harmony 



MAXWELL ON THE COURSE OF STUDY 17 

with his environment impUes the development of cer- 
tain moral or ethical qualities; these may b-^ summarized 
under three great heads: Reverence, Courage, Simple- 
minded Devotion to Duty. 

The development of these virtues is necessary because 
without them no one will build surely and steadfastly 
upon the former achievements of the race. In other 
words, a man may know many things that are very use- 
ful, pleasant, and ornamental; he may know them well 
and thoroughly; but if he has no reverence, if he has 
no courage, if he has not simple-minded devotion to 
duty, his knowledge will be of little avail. 

24. Harmony with environment: physicaL — The 
third consideration in the adjustment of the child to his 
environment is the development of his physical powers. 
He must have health, strength, and agility of body, 
and skill of hand. A man may have knowledge, he may 
have these great ethical qualities of reverence and cour- 
age and simple-minded devotion to duty, yet if he has 
not health and bodily strength and some skill of hand, 
he will accomplish little. What will a man give in 
exchange for health? No amount of study, no amount 
of intellectual attainment, no amount of accomplish- 
ment in the purely intellectual sphere will ever compen- 
sate anybody for the loss of health. 

25. Summary. — These three things, then, are neces- 
sary to bring a child into harmony with his environment : 

1. Putting him into possession of his intellectual 
inheritance. 

2. Developing the three great moral qualities of rev- 
erence, courage, and simple-minded devotion to duty. 

3. Developing his health, strength, and agihty of 
body, and giving him the use of his hands. 



18 METHODS IN EDUCATION 

26. Extent of intellectual inheritance. — What things 
are included under the intellectual achievements of the 
human race? What is our intellectual inheritance? 
If this be determined, then the subjects that should be 
included in the curriculum of a school are known. And 
here we may follow a great thinker and fellow citizen, 
President Butler, of Columbia University. You will 
agree that his classification of the intellectual inheri- 
tance of the race is a comprehensive one: 

Literary inheritance, aesthetic inheritance, scientific 
inheritance, institutional inheritance, religious inheri- 
tance. 

Literature, art, science, institutions, religion, compre- 
hend the intellectual inheritance of the race. In the 
new course of study, each one of these great departments 
of our intellectual inheritance is represented. (Butler, 
The Meaning of Education, pages 3-34.) 

27. Literary inheritance. — Literature is represented, 
even in the very lowest grade, by the fables, and the 
folk stories, and the memory gems; in higher grades by 
the readers — and in the highest grades by masterpieces 
of literature. 

28. Aesthetic inheritance. — Aesthetics is repre- 
sented by the study of pictures, by drawing, by water- 
color sketches, and by music. In all classes, as is the 
case in a great many classes, photographs of fine pic- 
tures should be on the walls. They should, however, 
be there for some other purpose than simply to hang on 
the walls. They should not be pictures and nothing 
more to the pupils, but even so they just make some 
impression, if, as we fondly believe, the children are 
trained to some sense of beauty by merely looking on 
what is beautiful. 



MAXWELL ON THE COURSE OF STUDY 19 

Drawing, water-color sketches, and music serve to 
cultivate the aesthetic sense of the children, and the city 
itself presents also great opportunities for teaching 
children something of what is fine in architecture. A 
great deal can be done for this city by including some- 
thing of a taste for fine architecture. Examples of what 
is fine in architecture exist here side by side with ex- 
amples of what is most atrocious. For instance, the 
Flatlron Building is one of the most hideous structures 
in America, while only a few steps away from it may 
be seen one of the most beautiful buildings in this coun- 
try, a perfect gem of architecture, the Court House of 
the Appellate Division, at the corner of Madison Avenue 
and 25th Street. Many of our schoolhouses are speci- 
mens of good architecture, and those who live in other 
boroughs should take a journey up to the Bronx to 
see that beautiful building, the new Morris High School, 
which, situated on a hill, dominates the landscape. 

29. Scientific inheritance. — Our scientific inheri- 
tance is represented in the course of study by nature 
study, by mathematics, under which is included arith- 
metic, algebra, and inventional geometry, by physical 
geography, and by physics. 

30. Institutional inheritance. — Our institutional in- 
heritance is represented by political geography and by 
history, and it will be still better represented in the 
near future, when we come to study municipal govern- 
ment with more care than we do now. 

31. Religious inheritance. — Lastly, our religious 
inheritance is represented by ethical training, although 
the doctrines of any particular sect cannot be taught. 
This training comes partly from the habits built up 
through the administration of a well-ordered school, 



20 METHODS IN EDUCATION 

and partly from the study of all the subjects, particularly 
literature and history. 

32. Assimilation by child. — Now, if these five divi- 
sions of our intellectual inheritance should all be rep- 
resented somewhere in the course of study, the next 
question that comes up is, should something of each of 
them be taught from the very start, or should some of 
them be taken up later in the course? That is a nice 
question — a question upon which opinion will possibly 
differ, but for my part I have come to the conclusion, 
along with my colleagues, that some part of each one 
of these five great divisions of knowledge should be 
represented in every grade of the course. 

The opinion now held of a child's nature is more 
rational than that of years ago. In the little child, 
not more than four or five years of age when he first 
comes under your guidance, in that little body there is 
included the promise and potency of everything that 
afterwards develops into the full grown man or woman, 
just as a bud contains, in rudimentary form, the fully 
developed flower. The little child has a right to what- 
ever part of his inheritance he can assimilate; he is en- 
titled to have all of his powers developed from the start. 
Some of them will develop more rapidly than others, 
but all will develop more or less, provided they are 
supplied with the proper nourishment. 

33. Variety. — In the second place, the child mind, 
particularly in the beginning, craves variety. There 
can be nothing more dull and deadly, nothing more 
likely to check the development of a child's mind, than 
to occupy it all the time with one kind of work, or even 
with two or three kinds of work, particularly upon the 
formal sides of reading, writing, and arithmetic. If you 



MAXWELL ON THE COURSE OF STUDY 21 

would stupefy the child's faculties, if you would prevent 
his latent powers from developing, occupy him during 
his first years of school with a dull, monotonous routine. 
Only when the child has grown into a man does l\e de- 
vote all his time to one or two subjects. In the earlier 
stages he needs variety and he needs a broad founda- 
tion to support the edifice of specialization. Like the 
pyramids, the educational structure must be broad at 
tfie base and gradually taper to the top. 

34. Quantity of matter. — Some objection has been 
made to teaching so many subjects to young children. 
It has been said that they are given more than they can 
assimilate. 

The person who makes such a statement, either wil- 
full}^ misleads, or does not understand what is being 
done in the schools. In the primary schools, science is 
not taught as science, mathematics is not taught as 
mathematics, institutions are not taught as institutions. 
The child does not study these subjects separately. The 
child does not know the divisions of knowledge; he 
simply learns facts as facts. To put a flower into a 
child's hand and direct attention to its colors and parts, 
is to give him a lesson in botany; and this lesson is just 
as easily comprehended by the child as is a lesson on 
reading the word cat. Only very gradually he learns to 
classify and arrange facts in the separate departments 
of knowledge. 

Principles in Teaching 

35. Objectivity. — The next question arises as to the 
principle upon which the facts to be observed and taught 
should be selected and arranged. The first of these 
principles is familiar because it has been expressed in 



22 METHODS IN EDUCATION 

books upon principles of education and methods of 
teaching over and over again. Sometimes the expres- 
sion is ''from the known to the unknown, from the simple 
to the complex;" sometimes ''from the concrete to the 
abstract." The meaning underlying these expressions 
may be reduced to a form that will be our first principle: 
Select those parts of a subject that can be presented 
objectively or that will appeal immediately to the imag- 
ination of the child, for perception and imagination are 
the strongest powers in the young child's mind. 

36. Continuity, correlation, variety. — The second 
principle is the principle of logical unity or continuity 
in each of the studies; the third is the principle of 
correlation of studies, and the fourth is that of variety, 
or substitution. 

Application of Principles 

37. Objectivity. — The principle of objectivity is 
illustrated by presenting in the lowest grade arithmetic 
in the form of counting, objects of nature, birds, home 
geography, and striking anecdotes of great men with 
history. Just one word here, incidentally, upon a sub- 
ject that does not receive sufficient attention, home 
geography. 

While it is in one of the grades, 4A, home geography 
should not be limited to this grade, but should be used 
in illustrations wherever possible throughout the whole 
course. In lessons in geography, often no reference is 
made to things at the very door, and there are many 
who come out of our schools knowing very little about 
their own surroundings. A boy on the roof playground 
of one of the schools when asked, after the East and 
North rivers were pointed out to him, what waters he 



MAXWELL ON THE COURSE OF STUDY 23 

was looking at, said he saw the Atlantic and Pacific 
Oceans. 

Do not confine this home geography to one grade, 
but bring it in whenever it will illustrate the matter in 
hand. For instance the gutter in front of the school- 
house or the rivers that flow past this island will always 
illustrate the very interesting subject of river drainage, 
and the excavations being made in the city will illustrate 
the strata of the earth's surface. When you speak of 
forests, Prospect Park, Central Park, and Bronx Park 
furnish magnificent illustrations. By referring to Union 
Square, the plain may be illustrated; ask the children 
to imagine the square stretching out for hundreds of 
miles. Some of the parks downtown will give a fine 
opportunity to illustrate a desert. The usual way of 
illustrating a mountain by making a little sand heap 
on the sand tables amounts to little, because the propor- 
tion is lost; but if some of our Manhattan and Brooklyn 
friends could take their children down to Staten Island, 
for instance, and let them take a look at St. George, 
they would get a far better idea of what a mountain is 
than by the sand heap. Even by taking them to Morn- 
ingside Heights or by showing them the Palisades your 
object will be accomphshed. But objectivity is not 
then to be dropped. While geography lends itself 
particularly to illustrations, use illustrations in every 
subject — illustrations that are near and familiar to 
the child. 

38. Logical unity or continuity. — In arranging the 
various subjects in the course of study, the next thing 
to be considered after objectivity is the logical unity 
or continuity of these subjects; that is, the arranging of 
topics in such a way that one shall spring out of what 



24 METHODS IN EDUCATION 

goes before. With each advance, if possible, the rela- 
tion of cause and effect should be brought out, as in 
the production of wind through the expansion of air by 
heat, or the relation between the war of the Revolution 
and the French and Indian war. In this way alone can 
be established that wonderful connection between facts 
which make them part of the very texture of the mind. 
It is only when rational links of associations are estab- 
lished that knowledge stored away in the mind of the 
child will remain at its service. Teaching without 
establishing these links of association has resulted in 
very great harm to many characters. It has resulted 
in a lack of decision, simply because, when the decision 
was necessary, the link of association which would have 
enabled the individual to deal with the situation was 
not there. There is no more important work to do than 
to establish these links of association, which will bind 
together the masses of matter arranged under each 
topic from the beginning to the end of the course of 
study, and in so doing the very best possible means of 
insuring interest in the work has been taken as well. 

Compare for a moment two teachers. One of them 
takes no pains to establish the link of association, either 
by speaking of cause and effect, which is the best way, 
or by any other means. She simply says, '' I am going 
to hammer that knowledge into that boy's head if it 
takes me all summer;" and she hammers and hammers. 
What is the result? The child is not interested, and 
while she is doing her hammering he is thinking of his 
marbles or of his play. His mind is far away; he is pay- 
ing no attention, is getting into mischief, and perhaps 
the teacher thinks, in a moment of weakness — and per- 
haps the principal too — what a fine thing it would be 



MAXWELL ON THE COURSE OF STUDY 25 

if the inattentive boy could be sent to the principal for 
a walloping; and all because the teaching has not been 
done in the right way, for if the teacher were bringing 
out the relations between cause and effect, every child 
would be interested. Why is this true? Because this 
desire to know the cause of things, the desire to know 
the answer of the question, " Why? " is one of the pri- 
mary instincts of the human race. The child's mind 
cries aloud for the satisfaction of that instinct, and 
unless that satisfaction be given, the attention of the 
children will not be gained, and their minds will be 
with their games and play. Think of such questions as 
these, and the interest they may awaken: 

Why does the water rise in a pump when we lower 
the handle? 

Why does the mercury fall in the thermometer as 
the weather grows colder? 

Why does the dew gather on the grass at night? 

Why are railroads and rivers important in military 
operations? 

Why does dividing the denominator of a fraction 
multiply its value? 

By setting such problems and working at their solu- 
tion, interest is aroused and maintained because of the 
appeal to one of the most deep-seated instincts of our 
human nature. Such teaching is interesting and profit- 
able to children. But this is not all. By it is cultivated 
the habit of seeking for the cause* of events throughout 
Hfe. That is always the supreme test of good teaching. 
It is not whether the average is highest on the immedi- 
ate subject of study, but whether the child has acquired 
a habit which will be of use to him in life. Make him 
put the question, and make him try to answer the ques- 



26 METHODS IN EDUCATION 

tion, ''Why?" Then a habit is being estabhshed that 
increases enormously not only the efficiency of every 
kind of labor, but enhances the pleasure of living. Con- 
trast the laborer, for instance, who strings the electric 
wires, according to a rule, with a trained intelligence like 
that of Edison, which never rests without ascertaining 
the cause of every step in that operation. Which of 
them leads the more profitable and useful life? Con- 
trast the mind of a vender or seller of flowers in the 
street with that of an Agassiz or an Asa Gray. Which 
of them gets the most pleasure out of his work? Con- 
trast the mind of the navigator at sea who ascertains 
his position by rule of thumb with that of the naviga- 
tor skilled in the art of navigation who, by means of 
observations made on the heavenly bodies and the aid 
of trigonometry, can determine the position of the ship 
at any moment. Contrast the mind of the teacher 
who simply sets the task and listens, book in hand, to 
the recitation; contrast the mind of that teacher with 
that of the teacher who asks herself the reason for 
every step she takes and who sees in every mood that 
mirrors itself in her pupils' faces the manifestations of 
some all-pervading physiological or psychological law. 
By keeping the links of the chain tightly bound to- 
gether, by asking and inciting the pupils to answer the 
question, ''Why?" the links of association are being 
forged that enable the child to call up and use knowl- 
edge when it is needed; a perennial source of interest 
is being drawn upon that will enliven all school work, 
and a habit of mind is being cultivated that enhances 
the pleasure of life and increases its efficiency. 

39. Correlation. — The next principle is that of cor- 
relation of studies. We in America have not resorted 



MAXWELL ON THE COURSE OF STUDY 27 

to that form of correlation which is known as concentra- 
tion, in whose name so many educational sins have been 
committed. By concentration is meant the selection 
of some one subject, usually history, as the core of the 
course of study, every other study being arranged with 
reference to this core. 

While that principle has not been adopted anywhere 
in ^America, correlation is a very important and very 
useful principle. Correlation is not the teaching of 
two things at the same time — that is not the meaning 
at all, but it is using a fact or principle learned in one 
study, to illuminate or demonstrate something difficult 
of apprehension in another. Thus, grammar may be 
made to elucidate obscure or involved sentences in the 
reading lesson; stories from history brighten the details 
of geography, and the facts of geography explain, as 
nothing else can, the movements of history; while the 
knowledge acquired in arithmetic may be and should 
be used for quantitative work in every other subject, 
but particularly in science, civics, and geography. 

The difference between lessons based on correlation 
and those wherein no account is taken of this principle 
may, perhaps, be made clearer by the following illustra- 
tions. 

The Rose 

The teacher takes a rose from the hand of some little 
child who brings it into the classroom. She talks to the 
children about roses; they begin to get interested, when 
suddenly the lesson stops short, and from talking about 
roses they come to the reading lesson. How interesting 
it must be for that little child-mind in love with nature 
to be called upon to read ''See the dog has the rat! I 



28 METHODS IN EDUCATION 

see the rat. Does the cat see the rat? Can the rat 
see the cat?" There is not even a Httle variation in 
the way of an answer, such as, ''No, he can't unless he 
turns round." After a Httle while this is stopped, and 
the drawing lesson begins. No reference is made to what 
was done in the reading lesson. One child is drawing a 
square plinth, another is cutting out a dog, and so on. 
Such lessons as these are offences against correlation. 

How differently this work would go on with the help 
of a little correlation. The nature study begins as be- 
fore with the rose. Can any more beautiful object be 
used? Is there anything better to do than to place the 
rose in the hand of the child, and talk to him about its 
leaves and petals? He will learn to love it and learn to 
observe it. He will want to know something about it 
and find out what its various parts are. 

At all events, the teacher has interested the children 
in the rose. When the reading lesson begins, she does 
not begin to talk of the dog or the rat, but gets the 
children talking about the beautiful rose. And as the 
children talk she has taken some sentences that seem 
appropriate and pretty and has written them on the 
blackboard, and by the time they are through with their 
nature study lessons she has her blackboard covered 
with things they have said. What better reading lesson 
can there be than that? What could there be more in- 
teresting to the children? But the teacher notices that 
the things the children have said are not in very good 
order. There is no beginning or end. She says: ''Why, 
here is something about the color of the rose, and here 
is something about the perfume of the rose. Now, sup- 
pose we write these over." The children dictate, and the 
teacher puts the sentences together in order on the 



MAXWELL ON THE COURSE OF STUDY 29 

blackboard. She is letting the children talk instead of 
talking herself. They are simply dictating to her and 
she is writing. She makes no paragraphs. Something 
new comes up again about the shape of the rose, the 
number of petals, two or three statements about them, 
perhaps. She gathers these two or three statements 
together. They read the description again, and that is 
the^end of the reading lesson. 

Observe what has been done. The teacher has given 
the children the very best possible lesson. They have 
composed and she has written down. She has simply 
been their amanuensis, and without giving them any 
formal instruction she has got them to do the work. 
Then comes the drawing lesson, and the httle boxes of 
water colors are passed around with paper. What shall 
they draw? After this combined reading and nature 
lesson, would not the children like to make a picture of 
that rose, and would they not like to get one or two 
sentences from the board and write them under their 
picture? That is correlation. Is it not possible? 

In the higher grade the teacher was giving a read- 
ing lesson describing a place in England. Then she 
passed to the geography lesson; this was about Russia. 
Then she had the children reproduce something about 
Africa. The history lesson was about the French and 
Indian war, and the drawing was something that was 
not in the likeness of anything in the heavens above 
or the earth beneath. That is an example of lack of 
correlation in a higher grade. Here are a few examples 
of what seems to be legitimate, wise, and proper cor- 
relation: 



30 METHODS IN EDUCATION 

History and Geography 

In the first place, correlate history and geography, 
and don't do it by trying to teach two things in one 
lesson; but when giving the history lesson, use the 
knowledge of geography that the children have already 
acquired to fix every prominent place in the history. 
Correlate your geography lesson with the history les- 
son, for unless the child's historical knowledge is rooted 
to his geographical knowledge he will not retain it. 
Teachers make children memorize long lists of names 
over and over again. Of what use is it? The teacher 
should, however, be able to tell the story of any name 
associated with any great historical event. Tell some 
historical stories about Rome, Boston, Salem, New York, 
Concord, Vicksburg, Philadelphia, instead of trying to 
make the children memorize the names. Then again 
arithmetic should be taught with other subjects. Do not 
try to teach arithmetic when teaching nature subjects, 
but, whenever possible, correlate the work. It is a good 
thing to count the petals of the flower in nature study. 

Arithmetic 

There used to be an examination for graduation 
from grammar school. The children in most of the 
schools were splendidly drilled in arithmetic, but they 
had no idea of applying it outside of the arithmetic 
hour. 

This question was once given to a class: Supposing 
a piece of property — a house and lot — had an assessed 
valuation of $6000, and a tax of $26 per $1000, what 
should the annual tax be upon that house? All they had 
to do was to multiply the tax by six. Yet these children 



MAXWELL ON THE COURSE OF STUDY 31 

thought there was something wonderful about it, and 
covered pages in trying to get a wrong answer; and 
what was the reason? The teacher had not done quan- 
titative work, had not apphed their arithmetic and made 
them work out practical problems. 

Drawing 

Another proper method of correlation is to use draw- 
ing whenever possible. Use it whenever the child can 
better express his meaning in that way. Let him make 
a sketch right in the middle of his composition. I 
saw very recently a letter from a little girl who was 
taught in a school where this custom had been followed. 
This little girl — she is ten years of age — was describing 
to a little girl friend — she never knew I would see the 
letter — how another friend fixed her hair, and she found 
it hard to get the right words to express her ideas, so 
she drew a little pen and ink sketch. The little sketch 
was very good, and showed just how the hair was 
arranged. Use drawing whenever possible, and particu- 
larly in nature study, for there can be no proper study 
of nature without the objects, and no proper study of 
these objects unless they are drawn. This is absolutely 
essential. 

Language Work 

Another place where correlation may be apphed is 
in language work. To illustrate this, take the type 
sentences in one of the primary grades. It is an impor- 
tant thing for the teacher to know that all sentences 
can be reduced to five primary types, and it is impor- 
tant to the child — not to be told that there are five 
types — that information is not of any use to him; but 



32 METHODS IN EDUCATION 

it is important for him to know how to make sentences 
according to those five types. The first type of sentence 
is simplified by the expression, what things do, as, The 
dog barks, Birds fly; the second, what things are, as. 
Men and dogs are animals. The third indicates what 
quality things are; the fourth, what things do to things; 
and the fifth, what is done to things. All the material 
used in other studies can be introduced in the making 
of sentences after these models. All thought must be 
expressed by one or the other of these five forms, and 
in thus correlating the study of the sentence the work 
done in the other subjects is being reviewed, while at 
the same time the foundation for future grammar studies 
is being laid. 

Memory Gems 

There is another form of correlation by means of the 
memory gem — the thing the child memorizes. Corre- 
late this with the spelling lessons. Instead of dictating 
to the children every day, once in a while ask them to 
write from memory a few lines that they have learned. 
The selection of gems of poetry and prose laid down in 
the course of study was very wisely made by the com- 
mittee of principals. The children should learn these, 
and then write them from memory once in a while 
instead of taking dictation. 

Formal and Content Studies 

But here a very important question arises, one about 
which there is a great deal of discussion. Shall the for- 
mal studies, such as penmanship and the beginnings 
of arithmetic, be correlated with the content studies? 
Certainly, for it is the only way to make the child begin 



MAXWELL ON THE COURSE OF STUDY 33 

to recognize the symbols used for expressing the words 
in written form. Yet there can be no doubt that the 
best results cannot be obtained by teaching the formal 
studies only as incidental to the content studies. A 
lady who had quite a reputation as a teacher, and who 
loves her work, once said that when a child was learning 
to read she paid no attention to the formal side, but 
fixed all her attention on the content side, and that 
when the child did not know a new word she told him 
the meaning. The objection to that is that it does not 
develop power in the child. The child must be given 
some means by which he can determine the meaning of 
a new word when the teacher is not present to tell it. 
Literature cannot be enjoyed if the words are not under- 
stood, and no student enjoys the reading of a great 
work if he has to look up every word in the dictionary; 
no one can apply grammar to the correction of his own 
composition unless he has learned the classifications, 
the rules, and the definitions. In the first stage, there 
must be some reading, and the child will enjoy the study 
if it is well taught, if you will give him a reason for 
enjoying it. He enjoys a story, and if the story is read 
to him, he will show that he appreciates and enjoys it. 
He will want the book to get that beautiful story. By 
reading to him he gets the motive to read for himself. 
40. Substitution or variety. — The reason the prin- 
ciple of variety has been introduced is, first, that the 
children get tired of one subject. when they are kept at 
it too long, grade after grade. The new course prevents 
monotony. In the second place, the new matter is 
really easier for the child than the more difficult parts 
of an older subject. The beginnings of more than one 
part of the main divisions of study may be necessary 



34 METHODS IN EDUCATION 

in order to enable the child who no longer goes to school 
to adapt himself to his environment and to enable him 
to pursue his studies by himself. Enghsh history has 
been introduced in the seventh year, in the first place 
because the children get very tired of American history; 
and in the second place, because they understand and 
appreciate American history much better after studying 
English history for a year. Algebra and geometry have 
been put in the seventh year, so that the children may 
not get utterly tired of arithmetic, and may be able to 
use equations in solving the more difficult problems of 
arithmetic. These, very briefly, are the reasons for these 
substitutions. 



CHAPTER IV 
PRINCIPLES OF EDUCATION 

41. Justification of this cbJapter. — If any educator 
is inclined to question the appropriateness of a chapter 
on psychology in a text-book on methods in education, 
let him consider the necessity of giving a reason for every 
process in teaching. Reasons based on personal opin- 
ion or local success may be good, but the only reasons 
strong enough to command general acceptance are those 
supported by psychological principles of education. A 
knowledge of approved methods does presuppose famil- 
iarity with elementary text-books on psychology and 
principles of education, but surely there is no valid objec- 
tion to an attempt to unify the essentials of acquired 
knowledge in a book of this kind. The argument for 
convenience alone might be made a justification, but a 
better reason is the purpose of helping students who 
are trying to harmonize definitions of education, courses 
of study, psychology, and methods under a modern con- 
ception of effectual education. 

42. Limitations and options. — The terse presenta- 
tion of essentials in this chapter is intended as a guide 
to the interpretation of subsequent chapters, but no 
student is expected to consider these few pages a substi- 
tute for an approved text-book on psychology. In this 
matter, as in all other decisions on collateral study, 
the judgment of an earnest student is a safe criterion. 

35 



36 METHODS IN EDUCATION 

Other definitions may be preferred, too, but these 
are chosen on account of simphcity, directness, and 
brevity. 

Definitions 

43. Consciousness. — Consciousness is the name 
given to all possible mental operations. — Dexter and 
Garlick^s Psychology, page 2. 

Consciousness is that indefinable characteristic of 
mental states which causes us to be aware of them. — 
Halleck, Psychology and Psychic Culture, page 44. 

44. Mind. — Mind is a spiritual force that manifests 
itself in knowing, feeling, and willing. 

45. Knowing. — Knowing is the act of affirming the 
certainty of states of consciousness. 

46. Feeling. — Feeling is a term that indicates pleas- 
ant or painful states of consciousness. 

47. Willing. — Wilhng is the act of the mind in 
making a choice of desires. 

48. Will. — The will is the power which operates 
in the mind in willing. 

49. Faculties. — A faculty is a mental power which 
acts upon objects, external or internal, and discriminates 
them from one another. We must not, however, think 
of the mind as composed of separate faculties. The 
mind is a unit, but it can manifest itself in different ways; 
and for convenience we shall use the word faculties to 
indicate the different manifestations of power. 

50. Object, action, product of a faculty. — That on 
which the mind acts in the exercise of any faculty is 
termed the object of that faculty. I hear a peal of 
thunder; the sound so heard is the object of the faculty 
of hearing. The action of this faculty is called listen- 



PRINCIPLES OF EDUCATION 37 

ing; the product of such action on the object referred 
to is a notion or idea of the sound of thunder. — Welch, 
Teachers' Psychology, page 4. 

In teaching, the subject-matter of instruction is the 
object; the principles of education are appHed in the 
action; and the product is the ultimate purpose of all 
education. 

51. Attention. — Attention is the centring of the act 
of'any faculty upon its object, by an impulse of the 
will. — Welch, page 5. 

Consciousness occupying itself with an object is atten- 
tion. — Home, Psychological Principles of Education, 
page 314. 

Attention is that act of the mind by which we bring 
into clear consciousness any subject or object before the 
mind. — Gordy, New Psychology, page 111. 

Attention is concentrated ' consciousness. Attention 
is not a faculty of the mind; it is simply a concentra- 
tion of consciousness upon some particular object, 
external or internal. 

52. Interest. — Interest is the name given to the 
pleasurable or painful feelings which are evoked by an 
object or an idea, and which give that object the power 
of arousing and holding the attention. — Dexter and 
Garlick, page 31. 

53. Apperception. — Apperception is the process by 
which a mass of presentations assimilate relatively 
new elements, the whole forming a system. The new 
material assimilated may be either given in sensation 
or reproduced by the internal working of the psycholog- 
ical mechanism; and attention, in the broad sense 
of noticing an object, coincides in the main, but not 
altogether, with the apperceptive process. 



38 METHODS IN EDUCATION 

Apperception is the interpretation of new knowledge in 
the hght of that previously obtained: mental assimilation. 

54. Sensation. - — A sensation is a state of conscious- 
ness resulting from nerve action. — Halleck, page 59. 

A sensation is a simple mental state resulting from 
the stimulation or excitation of the outer or peripheral 
extremity of an incarrying or sensitive nerve. — Sully. 

55. Sense-perception : the gathering of percepts. — 
Perception is the general name of a faculty through 
whose action the mind gains knowledge, whether of 
things without or within ourselves. Sense-perception is 
the faculty which supplies the mind with knowledge of 
external objects through the action of the senses of touch, 
sight, and hearing. In exposure to a storm I see, hear, 
and feel the driving rain. In this act of sense-percep- 
tion the senses employed are those of touch, sight, and 
hearing. The object is the driving rain; the acts put 
forth are feeling, seeing, and hearing; and the product 
of these acts, while in progress, is a notion or percept 
of the rain. The percept in this case unites in itself 
the elements gained from feeling, seeing, and hearing. 
If the object of my sense-perception had been a thing 
which was visible but not tangible, or audible, as a pic- 
ture, a cloud, or a rainbow, the percept would have 
contained only the elements gained from the act of a 
sight. — Welch, page 5. 

56. Observation. — The special function of the senses 
is sensation, a responding to any external stimulus that 
affects nerve tissue. The corresponding function of 
the mind in referring these sensations to their external 
causes is perception. Sensation and perception taken 
together may be called observation. — Roark, Psychol- 
ogy in Education, page 68. 



PRINCIPLES OF EDUCATION 39 

Observation is the acquisition of knowledge by direct 
sense-perception. 

Observation is the act of looking at a thing closely 
so as to take note of its several details and parts. 

57. Memory: storing percepts. — Memory is the fac- 
ulty which unconsciously receives, retains, and restores 
the products or ideas gained through the action of the 
other faculties. — Welch, page 6. 

58. Imagination; building concepts. — The process 
of making images is imagination. An image is a revived 
percept. 

59. Conception: holding concepts. — Conception is 
a mental process which results in a concept. — Dexter 
and Garlick, page 150. 

60. Concept. — A concept is a re-presentation in our 
minds answering to a general name. — Sully. 

61. Judgment : connecting concepts. — A judgment is 
an assertion of agreement or disagreement between two 
ideas. — Dexter and Garlick, page 163. 

62. Reasoning : deriving concepts. — Reasoning is 
the faculty that derives new truths or concepts from class 
concepts already known. — Welch, page 11. 

63. Self -activity. — Self-activity, as a principle in 
consciousness, means self-direction. — Home, Philos- 
ophy of Education, page 171. 

Conscious effort in the evolution of possibilities is 
termed self-activity. — Boyer, Principles and Practice 
of Teaching, page 35. 

64. Habit. — A fixed tendency to think, feel, or act 
in a particular way is a habit. 



40 METHODS IN EDUCATION 

Training the Mind 

65. The plan simplified. — This topic is comprehen- 
sive enough to include the whole field of education. 
Students are confronted with conflicting the"bries about 
the possibility or impossibility of training the faculties, 
and then further conflict is found regarding effectual 
methods. Let us take it for granted that the term 
faculty, as defined in section 49, is used to indicate a 
kind of work done by the mind, without implying a 
division of mind itself; that each faculty can be trained, 
and that the general result is mental training. This 
mental training implies accompanying moral and phys- 
ical habits. All these habits constitute education. Let 
us see, then, how the plan can be outlined as a simple 
guide for our methods of training the mind. 

66. The plan outlined. — This working plan shows the 
faculties of the mind, or the manifestations of mind, 
which we have to deal with in educating the child; the 
laws or principles which guide the effort to bring the mind 
of the child into the desired relation with the mind 
of the teacher; and the object, aim, or result of all our 
efforts in education. 

Working Plan for Training the Mind 

PRINCIPLES OR LAWS 
FACULTIES OF EDUCATION RESULTS 

Sensation. Law of attention. Habit. 

Perception (Observation). Law of interest. Habituation to 

Memory. Law of apperception. right thinking, 

Imagination. Law of self-activity. right feeling, 

Conception. right willing. 

Judgment. 
Reasoning. 

67. Explanation of the plan. — Much attention used 
to be given to the natural order of development of the 



PRINCIPLES OF EDUCATION 41 

faculties. That order is indicated in the first column. 
In each faculty there are physical factors and psychical 
factors to be considered. The physical factors are the 
nerves and other material parts of the body; the psychi- 
cal factors are the mental or spiritual results of the 
respective processes. These matters are discussed 
under reaction. 

In every educational process there are certain prin- 
ciples of education to be observed. They are given in 
the second column. Thus in training any one of the 
seven faculties, all four of those principles should be 
used; and the order in which they are used is the order 
given in the second column. 

There are many aims in education, but it is possible 
to summarize all of them in habit. The process of form- 
ing habits is habituation. School life may only begin 
the process, but school life should direct the habitua- 
tion toward the right end. Think of all the purposes 
of education as you view them, and see if they are not 
all included under habituation to right thinking, right 
feeling, and right willing. 

Classification of Principles or Laws 

68. Lack of agreement. — The four laws mentioned 
in section 66 are not the only ones mentioned by those 
who have written on the principles of education. Her- 
bart could make apperception alone include all processes 
in education; apperception and self-activity can be 
considered adequate, since both attention and interest 
are contributing factors in both; others enumerate forty 
or more as essential laws. The classifications depend 
somewhat upon the purpose of the respective writers. 
One classification may be required irji a comprehensive 



42 METHODS IN EDUCATION 

treatment of the science of education, while another 
may be suited to psychology. The classification in this 
chapter is made to help students who need a simple 
but adequate guide for classroom work. While we 
favor the four given in section 66, others are given to 
satisfy educators who demand a wider classification. 

69. The principle of sense-perception. — This has 
been expressed by saying that the mind must gain 
through the senses everything external to itself; or, as 
Comenius said, " There is nothing in the mind that has 
not first been in the senses." As a principle in element- 
ary teaching, it is axiomatic. Out of this principle 
have grown the maxims, observation before reasoning 
concrete to abstract, it is better for a child to discover 
than to be told, empirical to rational, and others. The 
one large application is multiple sense instruction, or 
the necessity of appeaUng to as many of the senses as 
possible. Thus in a lesson the orange, the five senses 
are used as sources of sensuous impression. 

70. The principle of motor reaction. — The meaning 
of reaction is expressed in the maxims ''no impression 
without expression" and ''every idea tends to reahze 
itself in action." Happiness is expressed by laughing; 
grief, by weeping; and the rhythmic sensation of music, 
by dancing. So, too, every impression in teaching must 
have its complementary expression through verbal 
reproduction, written reproduction or material repro- 
duction as exemplified in the various forms of manual 
training. 

A brief explanation of the process is necessary. An 
external stimulus of any one of the senses is transmitted 
by the afferent nerve to the brain; if agreeable, the brain 
will receive the message and then transfer the message 



PRINCIPLES OF EDUCATION 43 

by an efferent nerve to the motor organs. Thus the 
brain is said to react upon sensations. It is the teacher's 
duty to present all subject-matter in such a way that 
each mind can receive favorable impressions. Then the 
mind will react, i.e., convert the impressions into action 
and thereby complete the process of getting ideas. 

James expresses himself thus: Regular response to 
stirgulation is reaction. Education as a process con- 
sists in furnishing proper stimulation and in directing 
the responses. Sensuous impressions are not properly 
educative if they fail to beget a correlative motor activ- 
ity. The physiological process is this: (1) impulse from 
external centre; (2) the translation in the central pro- 
cess; (3) the changed impulse is transmitted to the 
motor organ. — Talks to Teachers, Chapter V. 

Reaction implies a close relation between the phys- 
ical and the psychical. This relation shows the neces- 
sity of observing the physical conditions of the child 
himself, of the school and of the home. Little progress 
can be made in mental training if the child is hungry, 
fatigued, ill, or uncomfortable on account of light, heat, 
ventilation, or seating. 

71. The principles of attention and interest. — Atten- 
tion and interest are so closely related that one cannot 
persist without the other. Which comes first? Put 
your thought into practical ways of securing and retain- 
ing both and then answer the question by interpreting 
results. Attention is an attitude of mind and body 
growing out of and enforcing a feeling called interest. 
Both attention and interest are habits. 

72. The principle of apperception. — See definition 
in section 53. The educative value of a method is 
tested by the requirements of apperception. 



44 METHODS IN EDUCATION 

73. The principle of self-activity. — This principle 
exacts a distinction between teaching and telling. As 
the strongest impulse or instinct, it offers the largest 
field for reactions and stands as a law for both pupil 
and teacher. It is always a varying but true test of the 
vahdity of methods. 

74. Other principles. — The principles or laws of 
aim, induction, and deduction, analysis and synthesis, 
are discussed in the chapter on Methods of Teaching. 



CHAPTER V 
METHODS IN SCHOOL ECONOMY 

75. Meaning. — The rules, regulations, and laws 
governing the conduct of schools constitute school 
economy. The word economy implies a minimum of 
waste and a maximum of achievement. For details of 
this subject see Shaw's School Hygiene, Morrison's 
The Ventilation and Heating of School Buildings, 
Kotelmann's School Hygiene, and Button's School 
Management. 

76. Space. — At least one hundred twenty cubic feet 
of space should be allowed for each pupil. The general 
requirements for recitation purposes, physical exercises, 
coat halls, etc., vary according to local conditions, but 
convenience and comfort of pupils and teachers are two 
essentials in all schools. 

77. Light. — The light should come from the left 
hand side and somewhat above the level of the desk. 
Light from the right hand side causes the shadow of 
the hand to fall on the pupils' work; from behind, there 
is a larger shadow from the head and the trunk; from 
in front, the light is harmful to the eyes and round shoul- 
ders are caused by the pupils' bending down to avoid 
the direct glare. As a rule, light is permitted to enter 
from many parts of the room and then curtains or 
bhnds are used to regulate the amount and the inten- 
sity of the light. 

45 



46 METHODS IN EDCUATION 

Ventilation 

The average temperature desired is 64 to 70 Fahren- 
heit. 

The aim of ventilation is to remove impure air and 
replace it by pure warm air. From thirty to fifty cubic 
feet of pure air per minute are required for each pupil. 
Some means of securing ventilation from circulation 
are given in the following sections: 

78. Doors and Windows. — To be opened during 
marching, games, and recreation periods. *' Boards, five 
or six inches in width, placed under the windows are a 
well-known device. Still better are hoods at the top of 
the windows, closely fitting the sash, so that when the 
windows are open from the top the air is deflected toward 
the ceiling, and is gradually diffused throughout the room 
without falling too directly on the heads of the pupils." 

79. Air shafts. — Shafts leading from outside the 
building up through the floor to a height of six or seven 
feet. This height is required so that no draught will 
be felt by the children. 

80. Indirect method. — By the indirect method 
fresh air is carried into the building through large ducts, 
containing stacks of radiating surface, and directly into 
the rooms through registers which are usually placed 
near the ceiling. The impure air is carried out through 
a register usually placed directly underneath the incom- 
ing air, by means of separate ducts made somewhat 
larger than those provided for fresh air. Thus a school- 
room, heated and ventilated in this way, has a volume 
of fresh air constantly entering the room and an equal 
volume of impure air constantly passing out. — Button, 
School Management, page 62. 



METHODS IN SCHOOL ECONOMY 47 

81. Gravity system. — A gravity system is one where 
the draught necessary for withdrawing the foul air is 
caused by a heated chimney or duct. In every large 
building this method is not adequate or reliable, and 
ventilating fans are used either as a means of forcing 
the fresh air into the building, or of drawing out the 
foul air, or both. — Dutton, page 62. 

82. Fireplace. — A fireplace is a good ventilator, 
but not a uniform heater. 

Seating 

83. Adjustable equipment. — Adjustable seats and 
desks are the best. The seat should be adjusted at 
such a height that the pupiFs feet will rest on the floor 
while the legs from the knee to the thigh are at right 
angles to the trunk. The best adjustable desk has a 
slant of about fifteen degrees, but it can be raised to a 
level when necessary. Seats that are not adjustable 
are usually arranged according to definite sizes. 

Decoration 

84. Relation to school spirit. — This feature of school 
equipment has much to do with the spirit of the school. 
The walls and ceiling should be painted in some color 
restful to the eye. French gray, pale buff, and light 
green are approved. A few good pictures should dis- 
place a meaningless collection of cheap prints. Maps, 
diagrams, and the superior work of pupils are legitimate 
kinds of school decoration. Some teachers hold that 
maps, diagrams, and pupils' papers tend to distract 
the class by inviting attention away from the lessons, 
but a sounder view is that such diagrams have a high 
educative value from visualization during those periods 



48 METHODS IN EDUCATION 

when pupils naturally turn from study to relieve their 
minds. Compare James on mind-wandering, in Talks 
to Teachers, page 114. 

Grounds 

85. Suggestions from England. — These three para- 
graphs are quoted from Garlick's, New Manual of 
Method, page 6. 

Physical uses. — A playground is the lung of a school. 
It is as essential to a proper and efficient education as 
the schoolroom itself. It is the workshop for the manu- 
facture of the sound body, as the schoolroom is for the 
sound mind. It offers relief after mental work, and 
brings into play the overcramped muscles. It is a 
healthy agency for the overflow of that abundant spon- 
taneity of child life, which may become so troublesome 
to discipline if not regulated. 

Its moral uses. — It brings brightness to the school 
life and helps to engender a love for school by making 
it popular. It is a fine training ground for the emo- 
tions. Boys learn to discipline themselves in their 
sport, to submit their wills to the will of others. It 
is a great leveller and compensating force; for the dul- 
lard may be a physical adept. He wins in the play- 
ground the respect which he cannot attain in the school; 
for muscle is worshipped as much as brain. The bully 
is checked, the timid and shy get nerve and confidence 
by means of the playground's supervised play. 

The teacher^ s work. — Gymnastics should be encour- 
aged by the teacher, and, in the case of boys, a little 
instruction might be given. Supervision should always 
be exercised. The presence of the teacher will often 
tempt a boy to try something which otherwise might be 



METHODS IN SCHOOL ECONOMY 49 

beyond his inclinations. Games calculated to develop 
their strength, to give muscular control, to aid the growth 
of the will, such as our popular games, should be encour- 
aged, sometimes shared, and sometimes directed by the 
teacher. Many now form and take an active interest 
in the cricket, football, and swimming clubs of their 
scholars, and they do not find it unproductive labor. 



CHAPTER VI 
METHODS IN SCHOOL MANAGEMENT 

86. Opinions. — The worth of another man's opinion 
depends upon how much use we can make of it. Our 
own judgment becomes the court of last resort. Indi- 
vidualism is praiseworthy in an abstract theory of lib- 
erty, but there are times when the common welfare 
demands the acceptance of opinions of those who are 
competent to stand as authority. For this reason we 
quote certain passages. 

87. Principles. — The three essential principles under- 
lying school management in New York City are definite 
responsibility, free discussion, and spontaneity and orig- 
inality. These essentials were stated by Dr. Maxwell 
and discussed by him in an address in Brooklyn, Novem- 
ber 18, 1904. See sections 88, 89, and 90. These same 
principles may be applied in any other school system. 

88. Definite responsibility. — ''The first essential is 
definite responsibility. There should be a definite field 
of work, and I believe in looking to the person to whom 
the work is assigned, to do it, and not bother him in 
the doing. A principal should give definite work to 
do in the classroom, and should leave it to the teacher 
to do it, and not keep nagging her to death." 

89. Free discussion. — " The next essential is free 
discussion. If there is any difference of opinion, I 
believe the question should be freely discussed among 

50 



METHODS IN SCHOOL MANAGEMENT 51 

all grades of officers in schools. By officers I mean the 
teachers as well as the officers in the Hall of the Board 
of Education. I have very little use for teachers who 
come to me and say, 'Tell me just exactly what you 
would like to have done and I shall endeavor to do as 
you hke.' I hke to see a teacher who has the courage 
of her convictions; who is not afraid to tell me what 
she likes and what she does not hke in the course of study. 
We are all laboring toward the same end and should be 
united in the accomplishment of it." 

90. Spontaneity and originality. — " Third, I believe 
in spontaneity and originahty. Here in Brooklyn the 
teachers worked out many things with me which have 
been copied all over the country, and in many cases 
all over the world. Such was the method of studying 
Evangeline. We devised a way of correcting compo- 
sitions which would dispense with that most miserable 
method of teaching, sitting up nights to mark compo- 
sitions with red ink. Every one helped, and improve- 
ment was made possible by spontaneity and originality. 
The essential thing in carrying out the course of study 
is to make a wise selection of topics. Throw the non- 
essentials in the subjects aside and teach the essentials. 
Do not exact memorization of long lists of names which 
are in themselves meaningless. Two limits we must 
place on spontaneity and originality. We must not 
allow a person to be so original as to wish to try some- 
thing which in the past has proved a failure. We must 
never allow a teacher to make experiments which are 
beyond all reason. The development of the human mind 
is subject to law, and it is the business of the teachers 
to know the laws governing the development of the 
human intellect. Too often we do not know how or 



52 METHODS IN EDUCATION 

why certain things are accompHshed, the reason of the 
method or the object of the work; but in conies the phi- 
losophy of education to tell us why, to give us the reason, 
and to hold up before us that high grade of culture and 
life which it is the object of every good teacher to attain." 

91. Qualification of teachers. — Health, scholarship, 
character, and professional spirit are requisite qualifi- 
cations of the good teacher. The importance of each of 
these is not determined by the order stated, nor do we 
mean to say that other qualities are excluded. Fidel- 
ity, sincerity, fairness, sympathy, and other particular 
characteristics deserve discussion, but our limited treat- 
ment makes the four general qualifications include all 
such particular indications of merit. 

92. Maxwell on marking teachers. — As an illustra- 
tion of one detailed plan, we give in four sections an 
outline of an address delivered by Dr. Maxwell, June 
5, 1902. 

How to Estimate a Teacher's Value 

Teachers deemed fit and meritorious should be marked 
A or B; all others, C or D. The A mark should be 
reserved for teachers of conspicuous ability. 

93. Important things in teaching ability. 

1. Ability to impart knowledge, or power of exposi- 
tion. Do not do too much. Talking too much is a 
common fault. 

2. Ability to interest pupils. Without interest, 
teaching fails to become a part of pupil's make-up. 

3. Ability to train pupils to good intellectual and 
moral habits, i.e., character. 

94. Signs of poor teaching ability. 

1. Requiring parrot-like repetition of text-book. 



METHODS IN SCHOOL MANAGEMENT 53 

2. Most concert recitation is bad. 

3. Neglecting pupils' observing and inventing powers. 

4. Weak questioning. 

5. Neglect in use of object teaching. 

6. Waste of teacher's or pupils' time. 

7. Rate teacher's scholarship by her mastery of her 
subject, daily preparation, and interesting application 
of current events. 

Rate effort by her activity in school work and by 
her efforts to improve by study outside of school. 

95. Personality of teacher. 

1. Neatness and fitness of dress. No place for old 
society dresses. 

2. Pleasing tone of voice and clear enunciation. 

3. Sympathy for children. 

4. Decision of character. 

96. Control of class. — The only control to be marked 
meritorious is that obtained by interest in the work. 
Promise of reward, fear and repression deserve C or D. 
Repeated presentation of dishonest work by pupils is 
evidence of unfit control. 

Your general estimate of a teacher's ability need not 
be an average of your detailed marks. Bear in mind 
that the object of these ratings is not to fill columns 
with marks, but to do something to raise the teaching 
force of the city to a higher plane than it yet occupies. 

Program 

97. Suggestion. — Each school and every class in 
a graded school should have a daily program posted in 
a conspicuous place, and that program should be fol- 
lowed closely. This matter is so important that we 
think it necessary to give specific reasons. 



54 METHODS IN EDUCATION 

98. Teaching by suggestion. — When the teacher 
makes a program, posts it, and adheres to it for all 
periods of work and recreation, there is a silent sugges- 
tion for similar order in the life of every pupil. It is 
indirect instruction; it is suggestion; it is example. The 
worth of such systematic procedure is valued by pupils, 
and teachers will soon see that most of the pupils have 
made a neat copy of the entire program for individual 
desk use. By using a rubber pen the class program 
can be made large enough to be seen from any part 
of the room. 

99. The law of habit. — There is no need of blaming 
pupils for inability to study so long as teachers do not 
observe the psychological value of habit in studying. 
If we eat, drink, sleep, or attend to other physical needs 
at certain times, habit soon becomes so regular that no 
clock is needed to guide our wants. It is the same in 
mental habits. The study of mathematics at a cer- 
tain time puts the body and mind into favorable condi- 
tions for mathematics at that time every day, and no 
great variation in time can be safely made. Likewise 
for each study and for each recreation exercise on the 
program. 

100. The law of change or variety. — A good pro- 
gram alternates difficult and easy periods, puts memory 
processes in the morning, and places the shorter periods 
in the afternoon. This variety is not theory; it is a 
physical necessity. The problem of fatigue has demon- 
strated this. * 

Opening Exercises 

101. Justification. — Some teachers think the regu- 
lar work is so important that no time should be taken 



METHODS IN SCHOOL MANAGEMENT 55 

for morning exercises. This is a mistaken opinion. 
Ten or fifteen minutes in the morning will do more in 
the real work of education than hours in the facts of 
mathematics or grammar. Why? Look back to the 
purpose of education. The pupils enter school each 
day well or ill, happy or angry, industrious or mischiev- 
ous, as the case may be. There is lack of harmonious 
thoHght and action, lack of bodily and mental poise, 
lack of self-control. The one thing to do in education 
is to furnish the environment that will produce the 
desired conditions of mind and body. Books aside, com- ' 
fortable position, reasonable silence, respectful atten- 
tion, — these are conditions required for the morning 
exercises. These are the conditions that make the school 
a harmonious unit for the work of the day. Then fol- 
lows the reading of Scripture or other exemplary books, 
singing, current events, recitation, declamation, or 
brief talks by the teacher. 

102. Value of habit. — The value of opening exer- 
cises in arousing a good school spirit is manifest. A 
second value is in stimulating punctuality. Habit is 
here a development; it is always so. Personal experi- 
ence justifies some of the devices for overcoming tardi- 
ness. 

The aim is to get the pupils to school in time once so 
that the process of habituation may be started. Make 
the pupil conscious of that one success by commending 
him. Then try some of the motives and means men- 
tioned in the following sections. 

103. Memory gems. — Have a short, pleasing mem- 
ory gem on the board. Have pupils read it together, 
learn it together, and repeat it together. Social stim- 
ulus in this. Learn one or two each week. 



56 METHODS IN EDUCATION 

104. Desire. — Read a portion of an interesting story 
two or three times a week. This arouses desire to hear 
more. 

105. Interest in songs. — Sing the old home songs 
occasionally. Let pupils select the songs. 

106. Expectancy : declamation. — Have a short reci- 
tation or declamation occasionally. Put title and name 
of pupil on the board the day before, or simply announce 
that some one will recite. 

107. Monitors. — Appoint tardy pupil a monitor to 
act before school calls. He will be present. 

108. Motives. — Organize for marching, athletics, 
memory selections, singing, perfect attendance, — some- 
thing that will arouse class spirit in working under a 
motive. 

109. Anecdotes. — Read or relate an anecdote giv- 
ing the value of punctuality. Exalt the positive, the 
good; don't preach about the defects. '' My cook," 
said Washington, "never asks if the visitors have 
arrived, but if the hour has arrived." 

110. The teacher an example. — Teacher always 
punctual. Have a program and always follow it. 

111. Honor roll. — Roll of honor for good attendance. 

112. Fellowship. — The school is a social unity and 
every person in it owes a duty. Think, feel, and act 
so that no one can assume the right to be tardy. 

113. Our platform. — The selection of memory gems 
is matter that must be determined by the actual needs 
of the pupils. The platform given below has satisfied 
thousands of pupils. The use of the word platform 
invites a comparison or analogy; use civics and history 
in discussing party platforms. 



METHODS IN SCHOOL MANAGEMENT 57 

Our Platform 

1. The only way to have a friend is to be one. — 
Emerson. 

2. Be not simply good, be good for something. — 
Thoreau. 

3. No one can disgrace us but ourselves. — J. G. 
Holland. 

4. Heaven never helps the man who will not act. — 
Soyhodes. 

5. People do not lack strength; they lack will. — 
Victor Hugo. 

6. It is well to think well; it is divine to act well. 

— Horace Mann. 

7. Whatever is worth doing at all is worth doing well. 

— Chesterfield. 

8. Things don't turn up in this world until somebody 
turns them up. — Garfield. 

9. He that is good at making excuses is seldom good 
for anything else. — Franklin. 

10. I hate to see things done by halves. If it be 
right, do it boldly; if it be wrong, leave it undone. — 
Gilpin. 

11. The chains of habit are generally too small to 
be felt till they are too strong to be broken. — Samuel 
Johnson. 

12. Our greatest glory consists not in never falling, 
but in rising every time we fall. — Goldsmith. 

13. He that avoideth not small faults, by Httle and 
little falleth into greater. — Thomas d Kempis. 

14. It requires a good strong man to say: ''I was 
mistaken, and am sorry." A weak man hesitates and 
often fails to do the right thing. — Franklin. 



58 METHODS IN EDUCATION 

15. Labor to keep alive in your breast that little 
spark of celestial fire called conscience. — Washington. 

16. There are two freedoms — the false, where a 
man is free to do what he likes; the true, where a man is 
free to do what he ought. — Charles Kingsley. 

17. Let us have faith that right makes might, and, 
in that faith, let us to the end dare to do our duty as 
we understand it. — Lincoln. 

18. Some temptations come to the industrious; but 
all temptations attack the idle. — C. H. Spurgeon. 

19. Look not mournfully into the Past; it comes not 
back again. Wisely improve the Present; it is thine. 
Go forth to meet the shadowy Future, without fear, 
and with a manly heart. — Longfellow. 

20. Lord of the Universe, shield us and guide us. 

Trusting Thee always through shadow and sun! 
Thou hast united us, who shall divide us? 
Keep us, oh keep us, the Many in One. 

— Oliver Wendell Holmes. 

114. Grading. — The purpose of grading comprehends 
the welfare of the school, the teacher, and the pupil. 
For the school, grading is required as a means of adjust- 
ing work in the organization or the system. For the 
teacher, grading establishes a limit for the scope of the 
teaching. For the pupil, grading is intended as adapta- 
tion so that a maximum of progress may be guaranteed. 
The defects to be avoided are too rapid advancement, 
tardy advancement, and rigid systems not permitting 
adaptation to the needs of the pupil. 

115. Promotion. — Two aims in promotion are to 
advance pupils as rapidly as their attainments will 
permit, and to maintain a standard of approximate 
uniformity of attainment in the grade. Further con- 
sideration will be found in the next ten sections. 



METHODS IN SCHOOL MANAGEMENT 59 

116. Class teaching. — In our elementary grades 
there is much discussion about the relative merits of 
individual and class teaching, the effectiveness of group 
teaching, the practical apphcation of the Batavia plan 
and its usefulness in solving the difficulties of promotion, 
and, lastly, the separation and the special methods of 
instructing defective children. This section is inserted 
he^e to direct the attention of teachers to these topics. 
During any recitation period, is the class taught as one 
unified grade capable of understanding the teacher's 
presentation? Or, must each class be divided into 
groups and each group taught separately? Or, must a 
certain amount of individual teaching be done? Take 
individual and class instruction, for instance, and 
you will find that some educators say that the one 
cannot exist without the other, and that there are no 
serious difficulties arising under either if the teacher 
satisfies the ordinary conditions of teaching. This 
is a suggestive topic for students and we offer as a 
point of view that no matter how good the teaching 
may be, there will be some pupils who will present 
the necessity of individual instruction, either in or 
out of class. 

117. Group teaching. — Group teaching is not new, 
although it is so considered by some educators. It 
means nothing more than dividing the class into groups, 
according to ability, so that three groups, for example, 
shall be working on three respective kinds of assignment 
at the same time during one period. The teacher may 
be giving oral instruction to one group, while the other 
two are engaged in written exercises. This plan pro- 
motes adaptation of matter to the needs of the pupil, 
and so it becomes only a special illustration of one of 



60 METHODS IN EDUCATION 

the many characteristics of good teaching. Dr. Max- 
well's arguments in favor of group teaching are given 
in sections 118 to 125 inclusive. 

Arguments for Group Teaching 

118. General use. — It is now in general use in other 
cities — a strong presumption in its favor. 

119. Adapted to each pupil. — A teacher having, say, 
only fifteen pupils out of forty-five recite to her at one 
time is better able to distinguish the individual peculiar- 
ities of each pupil. 

120. Vigorous teaching. — The teacher being com- 
pelled to divide the recitation for each subject into three 
periods is constrained to conduct the recitation in a 
vigorous manner. She is forced to avoid the two most 
serious errors into which teachers fall in the conduct 
of a recitation: requiring children to recite verbatim, 
and talking too much themselves. 

121. Study periods. — Each pupil has abundant time 
in which to study in school. Complaints of overwork 
and excessive home study have practically disappeared 
wherever the group system is adopted. 

122. Concentrated attention. — The pupil learns not 
only to study, but to inhibit and concentrate his atten- 
tion — an invaluable experience for practical life. 

123. Promotion facilitated. — A pupil may be pro- 
moted just as fast or just as slowly as he ought to ad- 
vance. A pupil may be advanced from one group to 
another group within a grade; or promoted from one 
grade to another at any time in the term, without 
skipping any essential part of the work. 

124. No tiresome repetition. — One division should 
always be composed of pupils advancing more rapidly 



METHODS IN SCHOOL MANAGEMENT 61 

than those m the other, so that the teacher will not be 
compelled to repeat the same lesson on the same day. 

125. Difficulties and advantages. — The difficulty is 
to find profitable employment for the section or sections 
not having the oral lessons. Many teachers cannot 
teach unless every child's eyes are fixed on them. They 
cannot see that more than a minute of this kind of 
so-called attention is bad for the child. Some teachers 
fincl the system hard because they give three-fourths 
of their attention to the groups not reciting, trying to 
keep them " in order " and not realizing that more free- 
dom should be allowed children who are working by 
themselves as individuals. Some teachers believe that 
we divide classes only because the children have differ- 
ent attainments. They do not understand that we 
divide classes in order that the nervous strain on the 
children may be lessened, that they may feel that they 
are individuals, that they must not waste their time 
waiting for fifty to get a chance to read aloud or to 
spell or to compute, and. that they may have time to 
study. 

126, Individual teaching. — No matter what devices 
or methods or novelties may be advocated, the process 
of true teaching remains a personal relation between 
the teacher and individual pupils. The most success- 
ful class or group teaching is that in which the individ- 
uals in the class or group are able to put their minds 
into sympathetic communication with the teacher's 
mind, or vice versa. When the successful pupils have 
passed along with the satisfaction of a good degree of 
mastery, slow or defective pupils remain for individual 
teaching to give them the right of promotion. When 
any pupil fails to understand the instruction, when 



62 METHODS IN EDUCATION 

disorder interferes with the smooth course of teaching, 
when illness or other valid excuse causes absence, then 
there must be a personal meeting of the minds of teacher 
and pupil to restore conditions to a normal standard 
of efficiency. So under all circumstances it is safe to 
argue that individual teaching is the largest factor in 
the school education. 

127. The Batavia plan. — The Batavia plan derives 
its name from Batavia, N. Y., where it was devised and 
put into successful operation by Superintendent John 
Kennedy. This plan of teaching combines the best 
features of class instruction, group teaching, and indi- 
vidual teaching. The classes are divided into groups 
according to ability and two teachers are at work at 
the same time in the same room. One teacher is carry- 
ing on the regular work of the grade with the larger 
part of the class, while the additional teacher is instruct- 
ing one or more of the backward pupils. As soon as 
any pupil is capable of doing the next grade work, a 
promotion is made, no matter what time of the term it 
may be. This plan of promotion is used all through 
the elementary schools, and it is found that most of the 
defects in the ordinary systems of grading and promo- 
tion have been overcome in the schools of Batavia. 
Attention is directed to the special value of the individual 
instruction under the Batavia plan. 

Examinations 

128. For pupils. — This topic relates to the examina- 
tion of pupils although there is equal interest in the 
nature of examinations prescribed for teachers. A 
discussion of examinations for pupils is outlined in the 
next five sections. 



METHODS IN SCHOOL MANAGEMENT 63 

129. Methods of conducting examinations. 

1. By written tests. 

2. By oral tests. 

3. By combination of 1 and 2. 

130. Advantages of written tests. 

1. Self-realization, independence. 

2. Habits of industry in preparation. 

3. Basis of comparative valuation from time to time. 

4. Apperception, composition, correlation. 

131. Disadvantages of written tests. 

1. Not an accurate index of psychical progress. 
Other conditions — nervousness, lack of facility in ex- 
pression, etc. — are too strong. 

2. Too much time required from pupils and, later, 
from teachers. 

3. Cramming. 

4. Mental deceit: word vs. content. 

132. Advantages of oral examinations. 

1. Time saved. 

2. Personality of pupil and teacher united — real 
teaching. 

3. Practical preparation for life. Oral expression, 
prompt decision, co-ordination of mental powers. Habit. 

4. Attention and interest. 

5. Adapted to individual needs. 

133. Disadvantages of oral examinations. 

1. Time lost unless teacher is apt. 

2. Effects are transitory. 

3. Tends to guessing. 

4. Do not sustain class concentration. 

134. Reviews. — The lack of systematic and thorough 
reviews is one of the most serious defects in modern 
education. In their anxiety to cover the prescribed 



64 METHODS IN EDUCATION 

work, teachers devote most of the time to the presenta- 
tion of new matter and then pupils are expected to do 
the extra review and drill work outside of the recita- 
tion period. A safer plan is to devote at least two-thirds 
of the school time to drill or review work; the other one- 
third will be sufficient for presenting the advanced les- 
sons. The general characteristics of reviews may be 
considered under the headings in the outlines given in 
the last section. 

135. Home lessons. — It is said that there are five 
institutional factors in education: the home, the school, 
the church, the state, and the vocation. The effort 
to make the home and the school harmonize in relation 
to lessons assigned in school to be mastered at home is 
one unsettled problem in elementary and high school 
work. Many parents object to the assignment of home 
work on the grounds (a) that it is shifting responsibil- 
ity from the teacher to the parent, and (6) that overwork 
is likely to produce fatigue. The teachers, on the other 
hand, answer (a) that the school hours do not give time 
to cover the required work, and (h) that the habit of 
independent work is essential in the education of the 
pupil. For convenience in presenting a liberal view, 
both affirmative and negative, an outline is submitted. 

136. Advantages of home study. 

1. Habits: obedience, industr}^, self-activity. 

2. Criterion: honest work is an index of pupil's power. 

3. Co-operation: parents become interested. 

4. Review: valuable impression and expression of 
recitation work. 

5. Protection: keeps pupils at home. 

137. Disadvantages of home study. 

1. Habits: incorrect work bad in effect. 



METHODS IN SCHOOL MANAGEMENT 65 

2. Not a criterion: too much dishonesty. 

3. Friction: some parents disapprove. 

4. Fatigue: due to overpressure. 

5. Recreation: pupils need outdoor exercise. 

Moral Education 

138. A contribution from New York City. — These 
sixteen sections are taken verbatim from The Course of 
Study, 1905. 

139. Moral Aim. — It should be the aim of teachers 
and principals to make the life of the school, in every 
activity and relation, count for moral education. This 
aim should vitally affect not only the teaching of every 
subject and the treatment of every problem of discipline 
and training, but also the general atmosphere and spirit 
of the classroom and of the school. In working toward 
this aim, the following suggestions will be found useful. 

140. Personality of teacher. — The personality of 
the teacher is at the root of all moral education in the 
school. The teacher's voice, speech, bearing, and dress; 
the teacher's poise, self-control, courtesy, kindness; the 
teacher's sincerity, ideals, and attitude toward life, are 
invariably reflected in the character of his pupils. 

141. Reverence. — Reverence is vital to morality. 
Whatever quickens in children the feeling of dependence 
on a Higher Power; whatever leads them devoutly to 
wonder at the order, beauty, or mystery of the universe; 
whatever arouses in them the sentiment of worship or 
fills them with admiration of true greatness, promotes 
reverence. There is no subject studied in school which, 
reverently taught, may not yield its contribution to 
this sentiment. 

142. Self-respect. — Self-respect, which is also fund- 



66 METHODS IN EDUCATION 

amental to moral development, is engendered in a child 
when he does his best at tasks that are worth while and 
within his power to do well, with proper recognition by 
teacher and school-fellows of work well done. 

143. Principle in character. — The corner-stone of a 
self-respecting character is principle — the will to be 
true to the right because it is right, whatever the conse- 
quences, to act with firmness in the right as God gives 
us to see the right. The essential difference between 
principle and mere self-interest should be vividly brought 
home to each child. 

144. Spirit of school. — The spirit of the classroom 
and of the school — the spirit that makes children say 
with pride ''my class" and '^ our school" is one of the 
strongest of moral forces. Where there exists a proper 
esprit de corps, the problem of discipline is largely solved. 
Public opinion as a moral force should be moulded and 
utilized in every school. 

145. Social membership. — The child should early 
gain the idea of social membership. The truth that co- 
operation and unselfishness are essential to true social 
living should be made real and vital. This truth is 
brought home through ''group work" where the work of 
each is necessary to the work of all; and through the 
feeling in a school or class that the honor of all is in the 
keeping of each. 

The child should also learn that he is a meml^er, not 
only of the school, but of the family, of the neighborhood, 
of the city, and of the state and nation. What it means 
to be a loyal member of these social institutions should 
be made clear. The naturalness and the necessity of 
obedi.ence and of helpfulness should be shown. The 
moral aspect of home tasks, and of working with the 



METHODS IN SCHOOL MANAGEMENT 67 

departments of health, parks, street cleaning, police, 
and education, and not against them, should be enforced 
by concrete appUcations. In general, the truth should 
be impressed that without loyal and effective social 
membership no individual can lead a complete life. 

146. Self-government. — No person has a fully devel- 
oped moral character until there has been a transfer 
of the seat of authority from without to within himself; 
a moral man obeys himself. Each child in every grade 
should be steadily helped towards self-direction and self- 
government. Effective means to this end are: appeals 
to initiative and resourcefulness; the development of 
such a sense of honor as will preserve order without 
surveillance; and some form of organization designed to 
quicken and exercise the sense of responsibility. To 
trust a child tends to make him trustworthy. A system 
of pupil self-government, if wisely applied and not en- 
cumbered with unnecessary machinery, may be found 
effective. The form, however, of the organization is 
immaterial. The essential point is that the teacher, 
himself a member of the community, should make his 
pupils sharers to a certain extent in the problems arising 
out of their community life; and that he should intrust 
to them as members in their own right of the social body 
the performance of certain functions. Such training 
in social activity is effective training for citizenship. 
Under such conditions ''good order" will mean not so 
much the refraining from disorder as the condition of 
effective co-operation. 

147. Moral values of studies. — Each school study 
has a specific moral value. Literature and history em- 
body in concrete form moral facts and principles, show- 
ing to the child his own self ''writ large," furnishing him 



68 METHODS IN EDUCATION 

with ideals and incentives, and moulding his moral 
judgment; and they will accomplish these results the 
more surely as the teacher is himself moved by that which 
is presented. Every subject involving observation and 
expression is essentially moral. Every subject, there- 
fore, should be so taught as to make for truth-telling in 
word and act, and for training in self-expression. 

148. Contemporary civilization. — In connection with 
the regular studies of the school, such aspects of con- 
temporary civilization as are of value for developing 
the social spirit should receive attention. Hospitals, 
societies for the prevention of cruelty to children and 
to animals, homes for orphans and for the aged and 
infirm, fresh air funds, and similar agencies for social 
service should be brought within the child's compre- 
hension as opportunity offers. Deeds of heroism and 
self-sacrifice done by firemen, policemen, soldiers, and 
other persons, should be presented and commended. 
The truth that success in life means more than mere 
money-getting can thus be brought home again and 
again. The contemplation of deeds of cruelty, dis- 
honor, and shame has a necessary, though subordinate, 
place in moulding moral taste. 

149. Topics for moral lessons. — The following list 
of topics affords subjects for many practical lessons in 
morals and manners: 

1. Duties to parents, brothers, sisters, and playmates; 
to servants and other employees; to employers and all in 
authority; to the aged, the poor, and the unfortunate. 

2. Conduct at home, at the table, at school, on the 
street, in public assemblies and in public conveyances. 

3. The common virtues, such as regularity, punctual- 
ity, self-control, cheerfulness, neatness, purity, temper- 



METHODS IN SCHOOL MANAGEMENT 69 

ance, honesty, truthfulness, obedience, industry, and 
patriotism. 

Principles of Moral Instruction 

150. Development. — The course of moral training 
is a development, in which the child is first led to act 
rightly and afterward to work from principle; he pro- 
ceeds from obedience on faith to obedience on principle; 
frmn regularity to faithfulness. The child also develops 
from egoism to altruism. His impulse toward self- 
interest normally develops earlier than his impulse to 
put himself in another's place. Upon the full develop- 
ment of the former stage depends the full development 
of the latter. 

151. Cultivation of imagination. — The culture of 
the imagination is a powerful aid in moral instruction; 
first, as the power vividly to picture consequences — 
to put yourself in your own place later on (foresight); 
secondly, as the power to ''put yourself in his place" 
(social imagination, sympathy). 

152. Employ self -activity. — In using literature and 
similar material for purposes of moral education, the 
teacher should not violate the law of self-activity. 
The child may resent having a moral drawn for him 
which he can draw for himself. He is the more likely 
to follow the principle which he himself discovers or 
formulates because it is his own. 

153. Positive vs. negative. — The most effective 
method in moral education is positive rather than nega- 
tive. A mind filled with worthy interests, high ideals, 
and helpful activities has no room for evil. Approba- 
tion more than censure leads to well doing. Love is 
a stronger and a better motive than fear. 



70 METHODS IN EDUCATION 

154. Supremacy of law. — At every stage of school 
life pupils should be taught that they live under inexor- 
able laws which they cannot violate with impunity — 
both physical laws and moral laws. Obedience is not 
optional: it is compulsory. Penalty follows law-break- 
ing as surely as night follows day, though the penalty 
is not always immediate. 

155. Discipline. — Discipline in school management 
has reference to mental, moral, and physical training 
that tends to secure the self-control of individuals. The 
general use of the term discipline in regard to human 
faculties means training that enables a faculty to do 
more efficient work than it would have been able to 
accomplish without the discipline. So in a larger sense 
disciphnary school management aims to develop all the 
useful characteristics of good citizenship. 

156. Authority. — There are writers and teachers 
who hold that respect for authority is not an American 
ideal. We do not agree. Constituted authority, wher- 
ever it may be, deserves constant recognition and respect- 
ful obedience. Authority is not tyranny; it is a natural 
and necessary guarantee of order in moral, religious, 
and civil life. The largest development of individual 
freedom is impossible Avithout some accepted standard 
of authority. Pupils should be taught, then, that it 
is their duty to respect and obey the authority in the 
school, in the home, and in the community. 

157. Co-operation of parents. — In another section 
of this chapter we have spoken of the five institutional 
factors in education. One aim of ideal training must 
always be to get those five factors into harmonious co- 
operation. It is not always possible to secure such 
assistance outside of the home, but it is possible to bring 



METHODS IN SCHOOL MANAGEMENT 71 

the parents into close touch with the actual needs of 
the school. This may be done by correspondence if 
it is not convenient to have personal consultations in 
the homes of the pupils. A visit has many advantages 
over correspondence because it is possible for pupils, 
teachers, and parents to meet in common and establish 
a balance of opinions relating to favorable and unfavor- 
able work in the school. A third means of getting into 
toiTch with parents is patriotic exercises or other school 
entertainments. The natural interest in the welfare of 
the pupils on such occasions is the strongest inducement 
to parents to present themselves at the place where 
the entertainment is to be held. Other means of becom- 
ing acquainted are found in . churches, local societies, 
and other established means of social intercourse in the 
community. 

Punishment 

158. Definition. — Punishment is a penalty for the 
violation of the rules of order. The old idea of punish- 
ment embodied the necessity of giving the pupils an 
equivalent for the wrong that had been done. The 
modern view of punishment looks to the reform of the 
pupils through the cultivation of desirable habits of 
activity. 

The tendency in theory and practice is against cor- 
poral punishment. What, then, can be substituted? 
As some penalty is in accordance with the supremacy 
of law, as expressed in section 154, we shall discuss 
some approved kinds of punishment. 

159. Detention. — The practice of keeping pupils 
in the schoolroom at recess, during part of the noon or 
after school, has the approval of many educators 



72 METHODS IN EDUCATION 

although it is severely condemned by others. The loss 
of pleasure seems to be the basis of the punishment. 
One serious objection to detention is on the physical 
side. If the pupils were allowed the privileges of phys- 
ical exercise during the recess periods, it is probable that 
some of the sources of disorder would find a natural 
outlet in the games. The pupil who is detained is not 
likely to be in a frame of mind suitable for continuing 
the work of the day after his companions return to the 
classroom. For these reasons detention cannot be widely 
approved as a form of punishment. 

160. Assignment of extra tasks. — The aim of this 
kind of punishment seems to be the development of 
intellectual power through the extra work. It is implied 
that the mental training will ultimately direct the child 
into points of view that will cause him to desist from 
further wrong-doing. On the other hand, the imposi- 
tion of extra school work is likely to lead the child to 
dislike that kind of work and also to form habits of care- 
lessness in performing the assignment. 

161. Demerit marks. — This penalty assumes that 
pupils are ambitious to secure high standings as an indi- 
cation of proficiency. Some pupils do have such ambi- 
tions, but their ambitions are easily crushed as soon as 
one demerit mark appears upon the record. Other 
pupils care nothing for marks of that kind and so the 
punishment is wholly external and has little or no effect 
upon them. 

162. Expulsion. — This should be used only as an 
extreme means of settling the difficulty. Expulsion is 
justified only when the pupil reaches a state of rebellion 
which cannot be treated without an injury to the class 
or to the school. Then it is considered prudent to 



METHODS IN SCHOOL MANAGEMENT 73 

remove the pupil from the presence of his companions. 
An adverse view of expulsion Hes in the fact that the 
child expelled is to be at hberty in the community and 
his idleness is hkely to lead to the development of bad 
habits. The relation of idleness and crime shows the 
futility of expulsion as a form of punishment in any 
community. 

163. Incentives. — The ordinary incentives are marks 
for* scholarship or conduct, prizes, decorations, school 
privileges, and public commendation. Some of these 
are forbidden in certain school systems because of the 
difficulty in doing justice in selecting the best pupils, 
or because such distinction tends to develop egotism 
and selfishness in place of altruistic virtues. These 
incentives are called artificial. 

In contrast to the artificial incentives are the natural 
incentives. The latter are respect for teacher, respect 
of class, school spirit, sharing school privileges, and per- 
sonal satisfaction in doing one's duty. These are natural 
because they are human. Each incentive develops a 
stronger feeling between the pupil and some other mem- 
ber of the school. The benefit is the consciousness of 
personal power growing out of self-activity. Notice 
how the community interest promotes attention, inter- 
est, and activity. 

164. Self-government of pupils. — All education aims 
at self-government of the pupils. The specific use of 
the word here relates to the various forms of pupil gov- 
ernment, in which the pupils themselves participate in 
the legislative, the executive, and the judicial depart- 
ments of school organization. In each system of this 
kind, the government is a republic. The School City 
and the School State are common forms. 



74 METHODS IN EDUCATION 

165. Public opinion in school. — Disorder in school 
is sure to arise if confidence is not established in the 
motives of the teacher and of the pupils. It is a mis- 
take for a teacher to think that a large number of pupils 
hke to do wrong; and it is unfortunate for pupils if they 
cannot consider their teacher a friend. The establish- 
ment of mutual confidence, the pleasure of morning 
exercises, the satisfaction of success in the studies, the 
interest in rhetorical exercises, and the fellowship of 
the school grounds and the afternoon walks, — all these 
will tend to develop a healthy public opinion in school. 

166. Evils. — Such school evils as carelessness, lazi- 
ness, tardiness, truancy, whispering, lying, cheating, 
stealing, impudence, and rebelUon should be displaced 
by desirable habits. Repression is only a temporary 
suspense; substitution is the sound process. 

167. Virtues. — The desirable habits to be substi- 
tuted in section 166 are accuracy, industry, neatness, 
pohteness, truthfulness, honesty, justice, punctuahty, 
co-operation, and obedience. The substitution is a 
matter of gradual habituation. 

168. Affiliated interests. — In speaking of natural 
incentives, in section 163, we referred to the sharing of 
school privileges. Such privileges are found in the 
affiliated interest which serve as useful means of educa- 
tion in addition to the work of the recitation. The vari- 
ous athletic interests, the debating clubs, the school 
paper, the musical and dramatic associations and the 
alumni associations are all helpful in keeping a strong 
school spirit. 

169. Adolescence. — Independence is a mental char- 
acteristic of adolescence. Management during this 
period is guidance. Follow these suggestions: 



METHODS IN SCHOOL MANAGEMENT 75 

1. Environment must be adapted to pupil rather 
than vice versa. 

2. Physical health is a predominant consideration. 

3. Pupils need direction and inspiration rather than 
ponderous knowledge. 

170. Fatigue. — During adolescence growth is so 
rapid that strength is not constant. In younger chil- 
dren, fatigue is produced by other causes. So far as 
fatigue relates to management, it shows the necessity 
for finding and removing physical causes of disorder. 

171. Devices in management. 

1. Use quotations. See Our Platform, section 113. 

2. Ask pupil to write an opinion of his own case. 
Furnish two or three questions to guide him. Assign 
to be done at home.. This causes introspection. 

3. Have pupils write a letter of advice to themselves. 
They will unconsciously expose their own weaknesses. 
This aid will show what treatment is best. 

4. Ask pupils to write a letter of advice to the pupils 
in the class one grade below. This work will bring out 
virtues and vices under the pupils' point of view. 

5. Assign a composition on '' My Favorite Teacher." 
The literary merit may be less interesting than the enu- 
meration of certain characteristics not admired in the 
teacher who assigned this theme. But whatever the 
opinions may be, this device is one more way of helping 
pupils to the habit of justly measuring themselves in 
relation to others. 



CHAPTER VII 
METHODS OF TEACHING 

172. Definition. — By method is to be understood 
that body of principles drawn chiefly from a sound 
psychology, which are applicable to all teaching; by 
methods are to be understood the special plans and de- 
vices to be used in teaching a particular branch or sub- 
ject. — Roark, Psychology in Education, page 267. 

A method of teaching is a series of teaching acts so 
arranged as to attain a definite end or result. — White, 
Elements of Pedagogy, page 137. 

Method is a guidance of the process of adapting cul- 
ture material to the needs of the child. — Monroe, 
Text-Book in the History of Education, pages 749-759. 

Thus we see t^hat in speaking of method or methods 
in education, we must consider an orderly procedure 
determined by three factors — the teacher, the nature 
of the subject-matter, and the needs of the pupils. 
The procedure is not so changeable as a manner nor so 
narrow as a device; it is as broad as the nature of child- 
hood, as fixed as the laws of race development, and yet 
as flexible as the needs of individuals. Methods should 
be thought of as a process embodying the blended move- 
ments of the minds from definite stages of development 
toward the ultimate possibilities in life. Thus we can 
set aside the old conception of method as a rigid stand- 
ard to which all pupils must conform, and in its place 

76 



METHODS OF TEACHING 77 

establish the pedagogical ideal of method as a guiding 
process that stimulates initiative, enlivens motive, and 
directs all activities toward desirable habits for life. 

173. Classification. — The attempt to classify methods 
of teaching under twenty headings is a source of con- 
fusion in theory and practice. The real difficulty hes 
in the fact that so many teachers think that each 
classified kind is a distinct method of teaching. While 
thts misconception may be removed after a few terms 
in the schoolroom, is it not economy for a young teacher 
to know at the start that one recitation may include all 
the known methods? In other words, tact fits the need. 
If we emphasize six kinds as comprehensive, all the 
other kinds can be subordinated. The six are analytic, 
synthetic, inductive, deductive, topical, and Socratic. 
A better classification, but somewhat in advance, is 
these four: analytic-synthetic, inductive-deductive, top- 
ical and Socratic. The full list is given, however, so 
that students may suit themselves. 

174. Conversational method. — This method is a 
natural intercourse between teachers and pupils. While 
its use is generally restricted to lower primary grades, it 
may be used in higher work. Its success depends largely 
upon the personality of the teacher. Speaking in ordi- 
nary tones is an indication of natural poise, and pupils 
will gladly adapt themselves to similar phases of think- 
ing and doing. It is a method that inspires confidence, 
invites co-operation, and makes the educative process a 
matter of personal communication between teacher and 
pupil. It was the method of Pestalozzi, Froebel, and 
Colonel Parker. It is frequently called a dialogue method. 

175. Development method. — This is another dia- 
logue method whose use extends over the whole field 



78 METHODS IN EDUCATION 

of education. It is especially adapted to early informa- 
tion lessons which aim at clear concepts and easy expres- 
sion. Its aim is to develop right habits of thinking; 
and by the use of suitable material, the child's interest 
is aroused so that the matter, the method, and the 
result have educative value. A further study of methods 
will show that this method really includes many others, 
such as, particular to general, known to related un- 
known inductive-deductive, etc. You will see that 
these methods shade into one another; they are not 
so many distinct methods. 

Caution. — Do not try to develop everything. If 
pupils give you the answer before you are half way along 
in your place of development, don't deaden their inter- 
est or waste your time by completing the developing 
process on that lesson. 

176. Lecture method. — This is useful in intermediate 
and higher grades, especially where the matter is brought 
up for discussion and other reproduction in succeeding 
recitations. A kind of lecture or monologue method 
is required in all primary classes before text-books are 
introduced. Narration, description, explanation, and 
definition are given by the teacher as models for imita- 
tion and reproduction. But let it be understood that 
the lecture method, strictly interpreted as a lecture, 
is suited only to mature minds. 

Questioning 

177. Bases. — The attempt to classify questions 
under the headings development, drill, review, examina- 
tion, etc., is putting considerable value upon external 
form again. There are differences, of course, but the 
tactful teacher may use all these kinds of questions in 



METHODS OF TEACHING 79 

any one lesson, even though the lesson is strictly a devel- 
opment lesson. If sound methods of teaching must 
always depend upon three factors — teacher, lesson, 
pupil — then sound questioning depends upon these 
same three factors, and the teacher will adapt the 
questions to the needs of the children. 

178. Consecutive questioning. — This plan follows 
the order of seating or roll. The advantage is economy 
of time, and this advantage is potent under a strong 
teacher. The disadvantages are inattention in class 
and possible lack of preparation of assigned work, 
especially by the pupils who can foresee their exemption 
from obligation to recite. These adverse criticisms 
presuppose a lack of working spirit in the class and a 
certain defect in the teacher. 

179. Promiscuous questioning. — This method of 
questioning is that in which the teacher does not follow 
order in seating or the order of the roll, but calls from 
different parts of the room as his fancy dictates. The 
advantage of this method is said to be in the fact that no 
pupil knows when his turn will come and so all are pre- 
sumed to be giving attention. The fact that a pupil 
has recited does not justify him in thinking that he will 
not be called a second or a third time. The disadvan- 
tage in the method lies in the loss of time in calling the 
names, in the exemption of certain lazy pupils, and in 
the probability that the best ones in class will be called 
upon more than those who do not show the same amount 
of eagerness to recite. 

180. Simultaneous questioning. — The simultaneous 
method of questioning is that in which questions are 
directed to the whole class and pupils are given time 
to think what the answer will be. Then the whole 



80 METHODS IN EDUCATION 

class or one pupil may answer the question while the 
others are thinking or answering with him. The 
advantage of this method is said to be that the atten- 
tion and the interest of all pupils are held during the 
time of asking the questions. In those cases where it 
means concert recitations it is possible that a large 
number of the pupils are not giving the required 
thought, attention, and answers as the general tendency 
seems to indicate. 

181. Development questions and review questions 
distinguished. — Development questions require more 
time in asking and answering; the order is generally log- 
ical; the answers are in complete statements. Review 
questions are rapid; not necessarily in logical order; 
answers may be brief. 

182. Rules. — A few rules for questioning will not 
be out of place. They may be stated as positive or 
negative rules. 

183. Positive rules. 

1. Questions should be adapted to the powers of the 
pupils. 

2. The wording of the question should be simple, 
clear, specific. This rule is opposed to puzzles, vague 
questions, double questions, universal questions. 

3. The order of the questions should be determined 
by the law of successive clearness. Questions logically 
arranged are not always suited to the child's mind. 
Question to promote progressive clearness in the child's 
thinking. 

4. Make the question as short as clearness will per- 
mit. 

5. Question to impress what the children know, not 
what they don't know. 



METHODS OF TEACHING 81 

184. Negative rules. 

1. Do not end a question with what. 

2. Do not ask questions that allow a choice of 
answers. 

3. As a general rule, do not ask questions that can 
be answered by yes or no. 

4. Do not ask a question that suggests the answer. 

5. Do not abuse the use of personal pronouns in 
questions. 

185. Weak questioning. — Some questions to be 
avoided may illustrate the rules under sections 183 
and 184. 

1. Vague questions. How was the battle of Gettys- 
burg fought? 

2. General questions. What do you think I saw on 
my way to school? 

3. Obscure questions. Cain you comprehend the 
complexity of civilization? 

4. Double questions. Where was Taft born and 
what service did he render in the Phihppines? 

5. Universal questions, similar to general questions. 
Where is London? 

6. Involved questions. Considering the facts in the 
Missouri Compromise, can you, a student of modern 
civic problems, trace the results in relation to the prin- 
cipal causes? 

7. Direct questions. Was Burgoyne successful at 
Saratoga? 

8. EUiptical questions. The best kind of questions 
is—? 

If any omission in a question causes a pupil to give 
more energy to the meaning of the question than to 
the answer, the question is defective. On the other 



82 METHODS IN EDUCATION 

hand, alertness may be stimulated by ellipses in rapid 
review questions. 

186. Socratic method. — This method is a specific 
kind of questioning. As used by Socrates, it was con- 
versational in tone. He elicited statements from others 
by two kinds of questions: one to convince of error; 
the other to develop truth. Socrates was questioning 
the Sophists who assumed to be masters of all knowledge 
and so the first part of the Socratic process was destruc- 
tive and ironical. Its purpose was to overthrow and 
ridicule the wrong opinion held by the pupil. The sec- 
ond part of the process was directing the mind by its 
own activity toward the truth, and preparing the mind 
to recognize and accept the truth. 

187. Value of the Socratic method. — The Socratic 
method accepts the pupil's point of view in thought 
and language; it keeps within the scope of the pupil's 
comprehension; every movement in thought necessi- 
tates self-activity of the pupil; it leads into a discovery 
of the new viewpoint, but it does not tell; it leaves the 
pupil at the threshold of truth, but does not force him 
to accept it. It is conviction through directed activity. 
Sometimes called maieutic, i.e., giving birth to ideas. 

188. Irony in Socratic method. — Irony cannot be 
safely used in teaching. Encouragement, not sarcasm, 
is what the average pupil needs. 

189. Limitations in use of Socratic method. — The 
Socratic method is adapted to all knowledge in which 
the pupil's experience is sufficient to enable him to reach 
the truth. Beyond this Umit it is not useful. 

190. Illustration of Socratic questioning in mathe- 
matics. 

Meno. Socrates, we come to you feeling strong and 



METHODS OF TEACHING 



83 



wise; we leave you feeling helpless and ignorant. Why 
is this? 

Socrates. I will show you (calling up a young Greek 
and making a Une in the sand). Boy, how long is this 
line? 

Boy. It is a foot long, sir. 

Socrates. How long is this Une? 

Boy. It is two feet long, sir. 

Socrates. How much larger would be the square 
constructed on the second Une than on the first line? 

Boy. It would be twice as large, sir. 

Under the direction of the boy, Socrates constructs 
two squares on the sand, thus: 



Socrates. How much larger than the first did you- 
say the second square would be? 

Boy. I said it would be twice as large. 

Socrates. But how much larger is it? 

Boy. It is four times as large. 

Socrates. Thank you, my boy, you may go. Meno, 
that boy came to me full of confidence, thinking himself 
wise. I told him nothing. By a few simple questions 
I led him to see his errors and discover truth. Though 
really wiser, he goes away feeling humbled. 



84 METHODS IN EDUCATION 

191. Illustration of Socratic questioning in grammar. 

— Take a familiar answer in sixth grade grammar, 
using this sentence: Lincoln was very kind to children. 
Teacher asks a class to tell part of speech of every word 
in the sentence. A pupil says very is an adjective. 

Teacher. You say very is an adjective. 

Pupil. Yes, very is an adjective. 

Teacher. Why do you call very an adjective? 

Pupil. Because very modifies an adjective. 

Teacher. What adjective does very modify? 

Pupil. Very modifies the adjective kind. 

Teacher. You have told me the use of the word very. 
After finding the use what led you to say adjective? 

Pupil. I thought of the definition of an adjective. 

Teacher. Give that definition. 

Pupil. Anything that modifies a noun or a pronoun 
is an adjective. 

Teacher. What noun or pronoun does very modify? 

Pupil. No noun or pronoun. Kind is an adjective. 

Teacher. Now, what is your conclusion? 

Pupil. Very is not an adjective. 

Teacher. Then what part of speech is it? 

Pupil. Anything that modifies an adjective must be 
•an adverb; hence, very is an adverb. 

192. Another illustration of Socratic questioning. — 
Teacher. Define a straight line. 

Pupil. A line that doesn't slant. 
Teacher. Draws slanting line on board. Is that a 
straight line? 

Pupil. Yes. # 

Teacher. Does it slant? 

Pupil. It does slant. 

Teacher. What is the matter with your definition? 



METHODS OF TEACHING 85 

Pupil. It is not accurate. 
Teacher. Why not? 

Pupil. A straight hne may slant and still be straight. 
Teacher. Correct your definition. 
Pupil A straight line is the shortest distance between 
two points. 

Answers 

. 193. The kind wanted. — The kind of answers given 
by pupils will depend largely upon the nature of the 
questions asked by the teacher. When all the condi- 
tions are adjusted to insure a fair amount of effort, the 
answers are an indication of intellectual progress. We 
shall discuss this topic under four headings. 

194. The educational value of answers. — The test 
can be found in the methods of mind training treated 
in chapter IV. A good answer is evidence of clear per- 
cepts, serviceable memory, good concepts, and some 
application of judgment and reasoning. Furthermore, 
a good answer is evidence of attention; it may indicate 
interest; it must utilize apperception; and it requires 
self-activity. One good answer is the beginning of 
habituation. Other good answers will, of course, tend 
to fix desirable habits of mental activity. 

195. Characteristics of good answers. — From what 
has just been said it is evident that a good answer re- 
quires the child to do some thinking. He must think 
to get a correct interpretation of the teacher's question 
and he must think again to furnish material for his 
own answer. Then follows another quality, namely, the 
use of good language in clearly expressing the answer. 

196. What answers should be received. — First, the 
good answers just characterized; second, answers which 



86 METHODS IN EDUCATION 

are partially correct providing there can be a division 
made in the answer required. This view is the one 
that gives credit for all that the pupil is able to do. 
The third kind of answer to be accepted is the one that 
is evidence of fidelity on the part of the pupil. The 
answer may not be correct, but the effort to make a 
correct answer deserves some commendation. Strictly 
speaking, a correct answer is the only one that can re- 
ceive full credit in the recitation, but as the process of 
teaching does not expect a satisfactory answer to every 
question, it is suggested that the other two kinds of 
answers receive some credit as the means of encouraging 
the pupils. 

197. What answers should be rejected. — Dishonest 
answers, guesses, and careless answers should not be 
accepted. They may satisfy certain standards of mark- 
ing, but they are not educative. Dishonesty may be 
due to laziness; or it may be a kind of unconscious devel- 
opment in schools where per cents have been used as 
the goal of education. In all these cases, require the 
pupil to work toward the desired answers. This is the 
only positive cure. A negative treatment may place a 
zero upon the register, but a zero does Httle or nothing 
to direct the average pupil into habits of useful effort. 

198. From the particular to the general. — This pro- 
cess was emphasized by Pestalozzi in these words: 

'^It is a chief business of education to pass from dis- 
tinctly perceived individual notions to clear general 
notions." Individual notions are notions or ideas of 
individual things. Each of the five senses furnishes 
sensations which the mind may or may not accept. 
As soon as the mind considers sensation by examining 
the object that caused the sensation, the mind gains a 



METHODS OF TEACHING 87 

percept of that object. This percept may be considered 
a particular or individual notion. Then the memory 
and the imagination work on these percepts, until the 
mind combines the percepts into a concept or general 
notion. 

In all early education the teacher strives to train the 
senses to see things, to observe things, so that the mind 
may get clear, accurate percepts as the foundation of 
knowledge. Concrete material in teaching is useful 
because the pupils can use more than one sense in 
observation. 

Illustration 

To teach the definition of a noun, write sentences 
on the board. 

Longfellow was a poet. 

Pupils like poems. 

Lincoln loved children. 

Do you know nouns? 

The presentation will lead pupils to see that each name 
word in these sentences is a noun; and so from seeing 
particular name words are nouns, they infer that in 
general name words are nouns. So this inductive 
lesson proceeds from the particular to the general. 
The same process is found in all elementary develop- 
ment lessons. 

199. Simple to complex. — The meaning of these 
words varies as individuals vary. We must take each 
child's point of view. What is simple for the teacher 
may be complex for the pupil. 

1. In language work, the simple things are the things 
the child knows. Talk about toys, pets, experience. 
Use short, simple, familiar words. 



88 METHODS IN EDUCATION 

2. In learning numbers, the process of scoring is a 
simple way of indicating a knowledge of the number 
concept, thus: 11 for 2 or two; 111 for 3 or three. 

3. The simple sentence is mastered before the com- 
pound or the complex. 

4. In music the natural scale is taught first. 

5. In nature study the plant as a whole is studied 
as one single, simple, living thing. Later the child will 
become familiar with the complex structure of the plant 
and the functions of its various parts. 

200. Concrete to abstract. — The abstract concepts 
cannot be formed without first having a concrete con- 
cept. Thus, an abstract concept of whiteness comes 
after associating whiteness with a number of white 
objects. Another reason for using objective or concrete 
teaching is the demand for multiple sense instruction. 
Seeing, hearing, feeling, and even tasting and smelling 
may be employed. 

1. Alphabet blocks as play in education. 

2. Warlike toys for Spartan children. 

3. Foot-rule and yard-stick in linear measure; gill, 
pint, quart, and gallon measures in liquid measure; 
ratio and proportion by handling blocks in Speer method. 

4. Moulding-board, putty maps, relief forms, and 
pictures in geography. 

5. The study of a model to get form, style, and rules 
in composition. 

201. From the known to the related unknown. — A 
child is master of considerable knowledge when he 
enters school. This knowledge in possession must be 
used as apperceiving groups as a basis for new knowledge. 
The adaptation of the old and the new will utiUze 
interest and attention. 



METHODS OF TEACHING 89 

1. The schoolroom, the playground or the city may 
each or all be used in early lessons in geography. This 
plan illustrates from the particular to the general. 

2. From knowing the agreement of subject and pred- 
icate, the child passes to concord of adjectives and nouns, 
pronouns, and antecedent, etc. - 

3. Unity in a sentence is a foundation for unity in 
paragraph and essay. 

4. Definition of a verb is necessary for an under- 
standing of the participle, and the nature of nouns and 
adjectives leads to the secondary nature of participle. 

5. The common denominator for addition of frac- 
tions opens a way to subtraction and division of frac- 
tions; and common fractions in general are a basis for 
decimals and percentage. 

202. Observation before reasoning; processes before 
rules; facts before definitions or principles. — The'se 
axioms are a demand for inductive processes in teaching. 
They are justified by psychology because percepts 
precede concepts, and definitions require related classes. 
Discovery aids activity. 

1. Window gardens are means of causing the child 
to discover the relation of hght, heat, and moisture to 
plant life. 

2. Five or more examples worked in multipUcation 
of decimals will lead to the rule. 

3. Actual experiments with levers will quickly im- 
press the rules regarding fulcrum, weight, and power. 

4. See also inductive method. 

203. From the empirical to the rational. — Science is 
organized knowledge; and before knowledge can be or- 
ganized, some of it must be possessed. Every study 
therefore, should have a purely experimental introduc- 



90 METHODS IN EDUCATION 

tion; and' only after an ample fund of observations has 
been accumulated, should reasoning begin. — Spencer, 
Education, Chapter II, page 93 of Kellogg's edition. 

So this rule means that knowledge must be gained 
wholly by personal experience. It embodies all of the 
other preceding axioms. We admit that pupils should 
learn much by their own efforts, but all subject-matter 
cannot be mastered in this way. Some must be taken 
on the authority of the teacher, as the deductions in 
history, economics, and advanced mathematics and 
science. Our criticism is that the rule should not be 
absolute because all subjects do not admit personal 
experimentation. 

204. Heuristic method. — This name is derived from 
a Greek word meaning to find; and so it is a method of 
directing instead of telling. By questions, directions, 
problems, and suggestions the child is encouraged to 
find out everything for himself by discovery. It is a 
constructive method which aims to promote self- 
realization. It is the method of discovery under 
sympathetic and intelligent guidance. 

Illustration 

A class is beginning the study of Asia. Without any 
lecturing by teacher or reading by pupils, turn to the 
map of Asia. Each pupil has a geography. Take a 
general view of surface; location, direction, and name of 
mountains. Next take drainage; rivers, running north, 
east, and south; hence, three great slopes; highlands and 
lowlands contrasted and located. Coast line, peninsulas, 
harbors noted. Conditions affecting climate and the 
probable modifying elements. Probable occupations, 
productions, and consequent states of civilization. 



METHODS OF TEACHING 91 

The second process is verification. Observation and 
inference in the first process beget hvely interest and 
active thinking, and then the verification by consulting 
the printed pages completes the first period of study. 
Contrast the old memory exercise in studying Asia. 
See last two sections in chapter on geography. 

205. Prussian method. — Hinsdale says that " teach- 
ing is bringing knowledge into due relation with the 
mind." In the effort to induce pupils to share willingly 
in all the activities of the school, the Prussian method 
puts the pupils and teacher under a feeling of equality 
in a kind of social participation. For instance, a les- 
son covers eight problems in arithmetic. All pupils 
are equipped for written work at desks. The teacher 
calls for the interpretation of the first problem, and 
several pupils in turn contribute their opinions. This 
arouses the social stimulus or the general feeling in favor 
of individual and class success. All begin the written 
solution; one is called to explain a step, another explains 
a second step, and so on. After reciting, each one con- 
tinues his written work. So every step is explained 
in interpretation, solution, and analysis; every pupil 
has shared in oral and written work; every problem has 
been solved and all the difficulties have been Cleared 
away. The tone is conversational, the manner is nat- 
ural, the work is interesting in process and results, and 
the spirit of a civic community has been experienced 
by all. This kind of education is living, and not a mere 
preparation for living. 

206. Inductive method. — A process of reasoning 
which estabhshes a general rule, definition, principle, 
or proposition based upon the knowledge of particular 
cases. In chapter IV we explained briefly that the nat- 



92 METHODS IN EDUCATION 

ural order in acquiring knowledge is percepts, concepts, 
judgments. This order is said to be the order of race 
development. Primitive man learned, through con- 
crete and individual experiences, certain facts which 
he later formed into general conclusions. For example, 
flint is good material for arrow-heads. Such knowledge 
became a general possession and each generation added 
to the general fund of knowledge. 

Illustrations 

Solving several examples in division of fractions and 
then deriving the rule for inversion of the divisor; study- 
ing sentences containing relative pronoun and ante- 
cedent, and then constructing a rule showing that the 
pronoun and antecedent need not agree in case; begin- 
ning the study of history at seven o'clock every school 
day for two weeks, and then noticing that the mind 
has formed a habit or rule of thinking about history 
daily at that hour. 

207. Deductive method. — A process of reasoning that 
starts with general rule, definition, principle, or propo- 
sition and shows its respective appUcation to particular 
cases. Thus in teaching grammar, have pupils learn 
definitions first and then apply them; in arithmetic, learn 
rule and then work examples; in geography learn defi- 
nitions of land forms and later look for illustrations. 

208. The inductive-deductive method. — Neither in- 
duction nor deduction can alone constitute a suitable 
method in a complete act of instruction. The two must 
be combined. On account of this necessity, some writers 
mean inductive-deductive when they use the term induc- 
tive method. Let the student remember, then, to com- 
bine these two processes in every development lesson. 



METHODS OF TEACHING 93 

A second point to be remembered is that these two 
methods are justified by psychology; they satisfy the 
working of the mind. Teachers hear much about the 
action of the mind in passing from particular to general 
and then from general back to particular. In develop- 
ing the definition of an adverb, the teaching emphasizes 
several adverbs in sentences. A knowledge of each 
adverb is a particular notion. Then the mind general- 
izes these particular notions and expresses the general 
nofion in a definition of an adverb. But this does not 
complete the process; the impression is not deep enough. 
In other words, this definition must be applied to other 
adverbs in sentences, and pupils must construct sen- 
tences containing adverbs. This application or drill 
completes the educative process by passing from the 
general to other particulars. Thus the inductive- 
deductive method makes a complete mental act in 
every development lesson. 

209. Analytic method. — This method proceeds from 
wholes to parts. In grammar, begin with sentence 
and proceed to parts of sentence. In literature, study 
the whole selection before considering paragraphs, 
sentences, and words. In primary reading, begin with 
sentence and go to words, letters, and phonics. In 
nature study, observe the plant or other material as a 
whole before studying its parts. 

210. Synthetic method. — The synthetic method pro- 
ceeds from parts to wholes. In grammar, begin with 
words and build sentences. In primary reading, the 
building of phonic elements into words is synthesis. 
In primary geography begin with the schoolroom, 
having the children make a map of it and understand 
how a map represents an object; thence proceed to the 



94 METHODS IN EDUCATION 

schoolyard, the street, the city and show upon the city 
and state maps all the children have themselves 
observed, including rivers, hills, mountains, etc. 

211. Comparison of analysis and synthesis. — Both 
relate to the action of the mind in dealing with individual 
things and the parts of those things. Analysis seeks 
to show the relation between the parts; synthesis empha- 
sizes the parts themselves and later shows their relation 
in construction. Both processes are required in every 
complete mental act. 

Important Distinction 

212. Individual things vs. classes. — There is a com- 
mon misconception about the difference between the 
inductive-deductive method and the analytic-synthetic 
method. Analytic teaching is considered identical with 
deductive teaching, and synthetic teaching with induc- 
tive teaching. This is an erroneous idea. Analysis 
and synthesis are employed in dealing with single things, 
and their parts — a word and its letters, a sentence and 
its elements, a method in reading and its steps, a subject 
like arithmetic and its constituent processes; induction 
and deduction are employed in dealing with more than 
one thing in working to or from classes or generalization. 
The inductive method does begin with one thing, not 
so much to ascertain the nature of the thing itself 
as to find the larger class in which the one thing belongs; 
and while the inductive comparison of one thing with 
another may seem to be a synthetic process, let it be 
noted that synthesis seeks to put the constituent parts 
of one whole into proper relations, but induction seeks 
to put several wholes into a proper classification. Like- 
wise analysis is confined to the relations between one 



METHODS OF TEACHING 95 

whole and its parts, while deduction passes from the 
large classification of many wholes down to the appli- 
cation to one thing. In other words, analysis and syn- 
thesis deal with individual notions, individuals or single 
things; induction and deduction deal with general 
notions, or classes. 

213. Topical method. — Subject-matter may be 
divided so that each heading will include material for 
a unit of discussion. The ordinary division into chap- 
ters does not always suit the requirements for class 
assignment or for individual discussion. A topic should 
be complete in itself and yet be one of the related parts 
in a larger division. 

The advantages of the topical method are convenience 
in assigning lessons, definite responsibility in recitation, 
and independence of pupil in thought and expression. 
The disadvantage comes only from abuse in which facts 
are disconnected and class stimulus is sacrificed to indi- 
vidual achievement. 

214. Discussion in class. — The topical method sug- 
gests the important topic in this section. As it is 
frequently an examination question, an outline is sug- 
gested in the next four sections. 

215. Advantages of discussion in class: 

1. Aids in retaining attention. 

2. Pupils learn to express thoughts without direct 
question. 

3. Teacher can get a broader insight into pupils' 
method of thought and general knowledge and associa- 
tions. 

4. Pupils may have a keener feeling of responsibihty 
concerning the success of the lesson. 

5. Fear of error is at a minimum. 



96 METHODS IN EDUCATION 

6. It is an inducement to thorough and comprehen- 
sive study, volunteered information, etc. 

7. Is not so restricted as a direct answer to a question. 

216. Dangers in discussions in class. 

1. The bright and precocious will monopolize the 
time. 

2. The lazy, careless, and indifferent take a vacation. 

3. Wandering from subject. 

4. Loss of logical sequence of thought. 

5. Disproportionate emphasis of minor points. 

6. Confusion of ideas due to lack of clear and defi- 
nite statements and the variety of answers. 

7. Encourages guessing. 

217. Directions for creating and profitably conduct- 
ing a discussion. 

1. Arouse interest in the question by association with 
previous ideas or by a healthy spirit of emulation, etc. 

2. Get various opinions even if an excellent answer 
has been given. 

3. Put the children on their mettle by speaking of 
the excellence of certain remarks. 

4. Encourage independent ideas by catching those 
who answer by following sheep fashion. 

5. When there is danger of guessing put a pointed 
why? or how? 

218. Characteristics of effective discussion: 

1. Interesting subjects. 

2. Unity of idea. 

3. Alertness. 

4. Subject alive with associations, concepts. 

5. Calls for thought. 

219. Text-book method. — This name was formerly 
given as a kind of reproach to teachers who followed 



METHODS OF TEACHING 97 

the matter and method of text-books. A reaction went 
to the other extreme of oral teaching. Now educators 
are trying to secure a reasonable average. 

The abuse of the text-book method required verbal 
memory of the contents. The extreme oral teaching 
has made pupils dependent upon the teacher. Pupils 
have become passive on account of not knowing what 
to study, where to find it, and how to study. 

Text-books should be used, and the prudence of 
teachers is a safe guide in avoiding extremes. 



CHAPTER VIII 
GENERAL METHOD 

220. Device, method, general method. — In the dis- 
cussion of methods of teaching, there is not enough 
distinction between a mere device and a method. A 
device is simply a tactful presentation of some part of 
the lesson. It is generally personal, particular; it may 
or may not work well with another teacher under dif- 
ferent circumstances. For instance, in teaching about 
a lock in a canal an ingenious teacher may have a wooden 
model made by himself or a pupil. This is strictly a 
device, and a commendable one, but not properly a 
method although it is entitled to classification under 
objective or concrete methods of teaching. Again, a 
teacher makes a chart of figures covering the ordinary 
combinations for rapid drill. It is a good device, but 
it is not a method. 

We have described some of the methods which are 
useful in regular teaching. Now we come to consider 
whether there is one general method that is applicable 
in all teaching. V If there is such a general method, it 
must be that there are general psychological laws which 
apply to the development of all human beings. We 
think there are such universal principles or laws and 
there is one general method. Right here we may empha- 
size a thought suggested in the preceding chapter in 
regard to the desirability of eliminating several kinds of 

98 



GENERAL METHOD 99 

methods by making a better classification. Strictly 
speaking, method in education is one composite process 
embodying all of the methods described in chapter VII. 
This view is upheld in a book recently pubHshed, Col- 
grove's The Teacher and the School, page 319: " In spite 
of all the diversity of subject-matter, text-books, school 
surroundings, and teaching devices, in spite of all the 
differences *in age, acquirement, and individuahty of 
pupils, there is a truly typical method of teaching which 
is, 'in the main, constant and capable of being adapted 
to nearly all subjects and classes. And this is so because 
the major movements of the mind are so common to all 
learners and because the fundamental laws of teaching, 
based as they are on the nature of the mind, are valid 
for all subjects and find application in every recitation." 

221. Herbartian view of the order of the mind. — 
" No matter what the study may be, whether Latin, 
mathematics, science, or some other, the mind follows 
a certain order. Through the old related experiences 
(first step, preparation) new individual notions are 
reached (second step, presentation); these are compared 
and their essential characteristics abstracted (third 
step, comparison), and the resulting general truth is 
worded (fourth step, generalization); this generalization 
finally receives application (fifth step, application.)" 

These five steps are known as the formal steps of 
instruction. These names are the ones used by Amer- 
ican writers in place of the four used by Herbart, namely, 
Clearness, Association, System, Method. A modified 
form is commonly used in making plans for development 
lessons and examination answers, as follows: 

I. Aim TIL Presentation 

11. Preparation IV. Application or drill 



100 METHODS IN EDUCATION 

222. Justification of the formal steps. — Prior to 
Herbart's time (1776-1841), the old faculty theory of 
Aristotle was the prevailing psychology. That theory 
held that the soul was endowed with higher and lower 
faculties which were entirely distinct. The general 
divisions — knowledge, feeling, will — were subdivided 
into capacities or faculties, each subdivision having a 
distinct individual function. In place of this faculty 
theory, Herbart put the conception of unified mental 
life and development. He argued that the soul is a 
blank at birth, not endowed with intuitive faculties, 
but having capacity for adaptation to environment 
through sense-perception. Mental development is the 
result of these perceptions of presentations. The inter- 
action of presentations passes through generalization 
to concepts, and then in turn to judgment and reasoning. 
In this development of a unified mind, the concept is 
the ideal; the process is apperception; and the result is 
a habit of thinking. Thus this formal method in a 
development lesson adjusts mind and matter for ap- 
perception and at the same time habituates the pupils 
to a desirable way of studying. Justification is claimed, 
therefore, since the process secures clear concepts, 
thorough apperception, and effectual habits of study. 

223. Preparation. — This step is an effort to make the 
pupils' minds ready to apperceive the new knowledge. 
It does not mean the teacher's preparation or the pupils' 
prior study although both are necessary and useful. It 
uses acquired knowledge as an apperceiving group by 
which the new knowledge may be assimilated. So the 
purpose of this preparation is to put the body and the 
mind into a receptive attitude, and to relate the new 
and the old so that attention and interest will be active. 



GENERAL METHOD 101 

In brief, it is putting mental, moral, and physical powers 
into harmonious co-operation with the teacher's efforts. 
How should such preparation be made? Agreeable 
opening exercises are the first contribution. In the reci- 
tation, it may be an anecdote, a description, a brief 
review of related work, or simply a statement of the aim 
of the lesson. During the day, brief physical exercises, 
the singing of a song, or even a two-minute visiting priv- 
ilege may dispel fatigue and adjust the minds to the 
required condition. Tact is the best guide. The one 
danger is in making the preparation too long, — a scat- 
tering of attention and energy. Sometimes it is best 
to go straight to the presentation. In this, let the minds 
of your pupils be the criterion. 

224. Presentation. — In this part of general method 
the teacher utilizes some of the specific methods dis- 
cussed in the last chapter, as the inductive-deductive 
method. The minds prepared in the first step are now 
getting needed individual notions. Watch the process 
of passing to general notions. 

225. Comparison or association. — The mind con- 
tinues the process of apperception by associating, com- 
paring, and contrasting the facts of the new lesson with 
the facts previously acquired. The mind here abstracts 
the essential characteristics of each notion presented. 

226. Generalization. — Now the notions so clearly 
distinguished in the previous step are classified in the 
form of rules, principles, definitions, laws, maxims, or 
tables. The mind has formed general notions, 

227. Application or drill. — We have seen that the 
purpose of instruction is the formation of general no- 
tions or ideas. But general ideas will not remain a 
possession without thorough drill. So this step requires 



102 METHODS IN EDUCATION 

impressive drill and application to practical life. It is 
the completion of each educative act, namely, the return 
from general notions to particular notions. 

Modification of Formal Steps 

228. Aims. — In writing lesson plans, it is always 
advisable to state the aim of the lesson first, although 
this law of aim is not one of the Herbartian steps. A 
few years ago teachers in training were told not to express 
the aim of the lesson for fear pupils would lose inter- 
est in the development. It was supposed that the 
anticipation of results would guarantee co-operative 
interest and that thereby the pupils would discover the 
essential purpose of the lesson. That view is not sound 
today; it exalts the process of the presentation too much. 
Better state the aim as a focal point for all lines of energy 
during that recitation period. 

229. Rein on aim. — Professor Rein, of the Univer- 
sity of Jena, was a follower of Herbart, but the Her- 
bartian doctrines were modified in many particulars by 
him. This opinion on the law of aim agrees with the 
current American view: 

" The pupil should know beforehand what is coming, 
if he is to bring all his powers to bear upon the work of 
learning; and it is easier to call out all his effort if he 
knows beforehand what is to be gained. To conduct a 
child along an unknown road, toward an unknown ob- 
ject by means of questions and hints, the purpose of 
which he does not see, to lead him on imperceptibly to 
an unknown goal, has the disadvantage that it develops 
neither a spontaneous mental activity nor a clear 
insight into the subject. Having reached the end of 
such a fine of thought the pupil looks about himself 



GENERAL METHOD 103 

bewildered. He stands at the goal, but does not see the 
relation that the result bears to the labor performed. 
He does not rise to that satisfactory mental activity and 
favorable disposition of mind which are stimulated by 
the pursuit of a clearly set purpose." 

230. Dr. Hervey on formal steps of instruction. — 
Dr. W. L. Hervey, a member of the New York City 
Board of Examiners, gave his opinion of these formal 
steps in the New York Teachers' Monographs, Decem- 
ber, 1900. The article is conservative and practical. 
He admits the validity of the opinion regarding general 
method and the movement of the mind, but he dis- 
approves a rigid observance of the formal steps. He 
emphasizes the point that the five steps need not come 
in the order in which they are mentioned, but they 
all should come somewhere in every complete act of 
instruction. He cautions teachers against making the 
preparation too long because he has observed that 
pupils' minds have wonderful powers of adjustment 
to a straightforward and even blunt approach. He 
thinks that preparation instead of standing alone at 
the beginning of the recitation occurs at each step in 
teaching; each step should prepare for the next. Good 
teaching from start to finish is steeped in preparation. 
Preparation is no more an antecedent of the first step 
than it is of the third; hence preparation may involve 
the presentation, thought, or application or all of them; 
and second, that each of these involves preparation. 
There are an infinite number of preparations within 
each method-whole, and there should be infinite vari- 
ety in the method of handling them. Nor is it neces- 
sary that comparison and generalization should hold 
rigidly to the order in which they are named, for 



104 METHODS IN EDUCATION 

we frequently ask children to think and afterwards 
to imagine. 

231. Dr. Hervey's conclusion. — " The human mind, 
(generally speaking) is not a blunderbuss. Yet from the 
direction for making lesson plans which I have known 
to be given to advanced classes by teachers of the form- 
alist type, it would appear that teaching the mind is 
precisely analogous to loading a brass cannon. Swab- 
bing, taking aim, loading with powder and shot, ram- 
ming home, setting off the fuse, all must come in a 
certain order not to be deviated from. Such a figure 
limps on both feet. In more senses than one it smacks 
of militarism. One who is appealed to by it belongs in 
a factory where things are made, or on the firing line 
where people are shot at, not in a school where minds 
grow and are fed. 

" Therefore, the best way, in my judgment, to profit 
by the doctrine is not to think chiefly of steps, or of 
sequence, or of separateness, or of junctions at which 
one must change cars for the next step — the best 
teachers when at their best are, I trow, not thinking 
about the formal steps — but to think chiefly of the ideal 
end of instruction, as being that happy state of pupils' 
minds in which, for warmth and resource, there are 
abundant stores of concrete imagery, and, for economy 
and serviceableness, there is organization-pigeon-holes, 
and tags, card catalogues and indexes, or if you will, 
generals, lieutenants, and privates, each knowing his 
duty, and each on the qui vive to do it. The formal 
steps are, then, so many ideals which the teacher must 
attain before his work is done." 

232. Colegrove on formal steps of instruction. — 
'/These so-called 'formal steps' do not form a strait- 



GENERAL METHOD 105 

jacket to fetter the individuality of the teacher, as some 
critics seem to think; nor, on the other hand, are they 
a Procrustean bed on which every recitation is to be 
stretched, for lessons consisting of arbitrary facts or 
unrelated ideas cannot be taught in this way. Like 
all general principles they admit of great variety in 
their application to details. They do not solve all the 
problems of method, but they do serve as a standard by 
which the teacher can measure the correctness of his 
daily practice, and, once mastered, they contribute very 
much to the teachers' skill, power, and success in 
instruction. It is a misnomer to speak of the 'five 
steps in the recitation,' for very often the whole 
recitation must consist of one or two steps only. 
Many consecutive lessons may consist of the fifth 
step alone." — The Teacher and the School, page 324. 

Illustration of General Method 

233. Illustrative lesson on attribute complement. — 

Attribute complement or attribute is known as predicate 
noun, predicate pronoun, and predicate adjective. 
I. Aim. To teach attribute complement. 
II. Preparation. Review definition of sentence, 
subject, predicate, noun, verb, pronoun, adjective. 
III. Presentation. Have these sentences on board: 

1. Birds sing. 

2. Happy children sing. 

3. The children are happy. 

4. Pupils become students. 

5. Lincoln was a good man. 

6. Longfellow was kind. 

7. Longfellow was a poet. 

8. It is he. 



106 METHODS IN EDUCATION 

9. This is an attribute. 
10. Who is it? It is I. 

Sentences 1 and 2 will impress some of the points 
covered in the preparation. Sentence 2 is an easy 
approach to the adjective happy in 3. 

All read the third sentence. Then individual answers 
on subject children and predicate are happy. Next 
get subject noun children and predicate verb are. Note 
that are alone is not the predicate; are happy is the 
predicate. 

Teacher. Covering word happy, asks one to read. 

Pupil. The children are. 

Teacher. Is what you have read complete or incom- 
plete? 

Pupil. It is incomplete. 

Teacher. Uncovers happy. Now is the expression 
complete or incomplete? 

Pupil. The sentence is complete. 

Teacher. What word makes it complete? 

Pupil. Happy makes it complete. 

Teacher. Happy is a complement. Write word on 
board; analyze it: complete + nient; ment — that which. 
Now define. 

Pupil. Complement means that which completes. 

Teacher. What part of the sentence is completed by 
happy? 

Pupil. Happy completes the predicate. 

Teacher. What part of speech is happy in sentence 2? 

Pupil. Happy modifies the noun children; hence 
happy is an adjective. ^ 

Teacher. What part of speech is happy in sentence 3? 

Pupil. The same; it is an adjective. 

Teacher. Yes; an adjective completing the predicate. 



GENERAL METHOD 107 

It is a predicate adjective. Another name is some- 
times given. If the children are happy, you can say 
that happiness is an attribute of the children. Thus 
for good children, goodness is an attribute; industrious 
pupils, industry is an attribute. So we may call happy 
a predicate adjective or an attribute complement. 

Teacher. Find another adjective used as an attri- 
bute. 

Pupil. Sentence 6, kind is an attribute. 

Teacher. Then, as far as you have observed, what 
part of speech may be used as an attribute? 

Pupil. An adjective may be used as an attribute. 

Teacher. All read sentence 4. Then proceed as be- 
fore to teach that students completes the predicate and 
refers to the subject. It is a noun used as attribute 
complement; or it is a predicate noun. Likewise for 
predicate pronouns, eliciting for each complement (a) 
that it completes the predicate, and (6) that it describes 
the subject or means the same as the subject. 

IV. Comparison. Pupils distinguish attribute from 
object. 

V. Generalization. Call for definition of attribute 
and, when suitable wording is secured, write definition 
on board. All read; individuals read. All define; 
individuals define. 

VI. Application or drill. Direct apphcation in such 
sentences as these. 

1. This definition is easy. 

2. Grammar is a useful subject. 

3. Easy is a predicate adjective. 

4. Emerson was a scholar. 

5. The wind feels cool. 

6. Who called? It was she. 



108 METHODS IN ^ EDUCATION 

Then apply by requiring contrast; thus: 

1. This is our school. 

2. We have a new school. 

3. Whom did you ask? 

4. Who was it? 

5. This work seems pleasant. 

For further drill, have pupils construct sentences 
containing attributes. It may be helpful to learn this 
hst of verbs which are generally followed by an attri- 
bute complement. 

be seem 

become feel 

appear look 

234. Method-whole. — The use of the general method 
requires a special classification of subject-matter. In 
order that we may apply the formal steps of instruction 
the subject-matter has to be grouped and classified into 
definite unities. Each unit of instruction is considered 
a method-whole. Thus in studying New York State 
all of the drainage could be put under an outline or clas- 
sification; and then this general outline could be divided 
for particular lessons each week or each day. So it is 
that each division may be treated as a method-whole. 
Gordy defines method-whole as a group of particular 
facts involving a universal. In other words, any topic 
or portion of a subject that constitutes a unity such 
that the process of teaching follows the inductive- 
deductive method is a method-whole. It should be 
noted in connection with this explanation of method- 
whole that the matter of general method, formal steps 
of instruction, particular notion to general notion, 
inductive-deductive method, and complete act of 



GENERAL METHOD 109 

instruction are all different names for one general prin- 
ciple underlying the Herbartian general method. The 
lesson on the attribute complement is an illustration of 
a method-whole. 

235. A definition of method- whole. — Each group of 
particular facts involving a universal is a method-whole. 
— Gordy, A Broader Elementary Education, page 197. 



CHAPTER IX 
SPELLING 

236. Accuracy a worthy aim. — As long as accuracy 
remains a requisite of success in life, correct spelling 
should be considered a vital aim in education. A theo- 
retical search for the causes of poor spelling may place 
the blame upon the pupil, the words studied, or the 
methods of teaching; but the practical accomplishment 
of spelling correctly will never come until teachers agree 
that spelling deserves to be taught as an individual sub- 
ject and not merely as an incidental study. Errors are 
too often excused on the ground that it is impossible 
for certain pupils to learn to spell, or that misspelling 
is a mark of genius. Better strive for accuracy as an 
ideal than to justify errors by excuses. 

237. Value of spelling. — It is not a culture study 
like history and literature, but it is a necessary art which 
is to be acquired in the most positive way and which 
is to become automatic as soon as possible. 

It is no particular credit to be a good speller, but it is 
a disgrace to be a poor one. Spelling, therefore, has a 
conventional value which may not be despised with 
impunity. — Taylor, Word Study in the Elementary 
School, pages 27 and 28. 

238. Psychology of Spelling. — It is a mistake to 
say that spelling depends upon the eye alone or upon 
any other single sense; spelling demands multiple sense 

110 



SPELLING 111 

instruction. In learning to spell, as in all other educa- 
tive efforts, the child should be taught to use as many 
senses as possible. One sense may do more than an- 
other, but one sense cannot accomplish the best results 
without the co-operation of the other healthy senses. 

This opinion is upheld by Dr. Shaw in his little book 
on Three Studies in Education. After discussing experi- 
ments with more than two thousand children, he ex- 
presses this conclusion on page 10: '' Spelling is largely 
a matter of association, and the eye, the ear, and the 
motor must be appealed to so as to produce the strongest 
complication of sensory elements. Care then in the 
right kind of oral preparation, with considerable oral 
test before writing, training pupils to build up words 
by using small unities into which words can be divided, 
is a method of teaching spelling productive of the best 
all-round results." 

239. The problem. — Poor spellers are found in every 
class. This is a fact, not a supposition. Our duty is 
to find the causes of the trouble, and then try to apply 
specific remedies. Pedagogy is not a panacea, nor is 
wholesale criticism a helpful aid to efficiency. There are 
difficulties in subject-matter, in pupils, and in teachers. 

Difficulties in Suhject-M alter 

240. Composite language. — The English language 
is a composite one, derived from a large number of other 
languages, and so there are many irregularities. For 
illustration, note the origin: depot, French; coffee, Ara- 
bic; banana, Spanish; waltz, German; sloop, Dutch; 
drink, Anglo-Saxon; gale, Scandinavian; manual, Latin; 
epistle, Greek. The principal difficulties are the fol- 
lowing : 



112 METHODS IN EDUCATION 

1. Silent letters. 

2. Language not phonetic, i.e., spelling different 
from sound; as, eight, phonic, praise. 

3. Different pronunciations for same combinations 
of letters; as, ou in ought, soul, bough, etc. 

4. The numerous sounds of the vowels. One edu- 
cator puts ninety-five per cent of all errors in spelUng 
under this head. 

Difficulties in Pupils 

241. Not knowing how to study. — In every lesson 
there are certain words which the pupils already know. 
In spelling, as in all other subjects, the process should 
be one of separating the known from the unknown so 
that the child may direct his energy toward what he 
does not already know. Habituate pupils to this pro- 
cess of selection so that they may devote their energy 
to the mastery of the new words in the list. Notice, 
too, the specific difficulty in each word. Can the word 
be spelled phonetically? If not, why? The answer 
will direct attention to the difl[icult3^ Homonyms illus- 
trate this difficulty. Where is the accent? Pupils 
rarely misspell any accented syllables because the em- 
phasis has impressed those syllables upon sight and 
hearing. Hence, observe the unaccented syllables for 
visualization. 

242. Failure in observation. — Take the pupil apart 
from the class for personal instruction. Test him on 
a few words to find his difficulty, and it is probable that 
the difficulty is in not seeing the word exactly as it is. 
Take two or three words apart from the printed or writ- 
ten exercise and encourage him by having him master 
these few words by oral and written effort, and then give 



SPELLING 113 

him credit for every indication of progress. This is a 
special effort in the formation of right habits of study, 
and every progress made by a defective pupil will be 
an encouragement that will work its own reward. A 
persistence in right habits will overcome the defect in 
failing to see the word exactly as it is printed or written. 

243. Carelessness. — Try visuahzation. Write five 
words on the board. Have pupils look intently at them, 
then cover or erase the words and let pupils try to write 
the list in order. A few exercises of this kind will direct 
attention to the difficulties in each word, the order of 
the words and their particular relation to one another. 
An entire lesson can be learned by a whole class in a 
short time in this way. It is another means of pro- 
moting the social stimulus advocated by Dewey. 

Difficulties in Teachers 

244. Defective teaching. — The third cause for poor 
spelling can be found in the teachers themselves. In- 
stead of making an adverse criticism in general, let us 
consider ten specific waj^s in which a teacher may fail 
to make a pupil get a complete, accurate grasp of the 
words in spelling. 

245. Using eye alone. — This plan has produced 
some excellent results, especially under the process 
called visualization. Pupils have acquired habits of 
silence, intensive apphcation, interest, obedience, and 
mastery. Such pupils are called eye-minded, a rather 
vague classification for children who are endowed with 
capacity for intelligent observation. When failures 
have to be explained, we are told that some pupils are 
ear-minded. This is another instance of juggling with 
terms, a practice that has associated pedagogy with 



114 METHODS IN EDUCATION 

nonsense. An elementary knowledge of mind is enough 
to make us understand that the mind of any normal 
child retains and reproduces an idea more easily if the 
impression of that idea has been enforced by as many 
senses as possible. For this reason, the good teachers 
encourage the use of eye, ear, tongue, and hand. The 
child is denied none of his natural rights, and, in most 
cases, the results are satisfactory because the using of 
all of those powers together produces an effect much 
stronger than the total effect of appealing to those 
powers one by one. 

246. Rote work. — The memory is overtaxed by 
learning lists of unrelated words. The remedy is in 
turning to words used in conversation or in the daily 
lessons. 

247. Neglect of spelling as a subject. — Spelling can 
never be satisfactorily taught as an occasional exercise 
in connection with other subjects. It can be correlated 
in this way, of course, but it deserves a place as an 
individual subject in the regular program. 

248. Abuse of dictation. — It is an abuse of dicta- 
tion to use it for purposes of drill or review before pupils 
have mastered the spelling of new words. The term 
dictation as used here has reference to the teacher's 
reading of certain sentences to be written by the pupils 
for the purpose of testing the pupils' knowledge of the 
spelling and the use of the words in the assigned lesson. 
Premature use of dictation leads to confusion instead 
of clearness. The evident remedy is to make effectual 
study of the lesson prepare for effectual application. 
Then the habit of learning spelling will require dictation 
as a process supplementary to the intensive study of 
the words, — a process that will prove to be effectual 



SPELLING 115 

because it brings into use all of the available powers 
of the child. 

249. Indistinct concepts. — The meanings of words 
are given as dictionary definitions. Encourage pupils 
to give their own expressions and applications. This 
is a suggestion for the use, not the abuse, of the dic- 
tionary. 

250. Lapses. — Infrequent recitation periods and 
lack of varied and thorough drill. This failure to give 
adequate drill is one of the serious defects in modern 
education. Is not repetition a fundamental law of 
habit? 

251. Unscientific classification. — Classification of 
words according to the number of syllables. This is 
unscientific and uninteresting. Use grouping under 
comparison and contrast. 

252. Interruption. — Trying to teach spelling when 
the child's mind is unprepared. Do not interrupt 
connected thinking in other subjects to correct a mis- 
spelled word. Keep the word for a special list. 

253. Lack of variety. — Failure to use a variety of 
interesting drills involving competition such as spelling 
down or choosing sides. See section 33. Remember 
the necessity of satisfying instincts or impulses if we 
wish to secure reactions. 

254. Excuses for failure. — Permitting pupils to 
form the habit of thinking that correct spelhng is impos- 
sible. The will is weakened every time we permit 
pupils to substitute excuses for effort. 

255. What words shall pupils spell? — Some favor a 
list of words selected from the pupils' vocabulary and 
from the lessons of the grade, while others advocate the 
use of a spelling book. In either case, the present 



116 METHODS IN EDUCATION 

tendency of opinion seems to be this : It is sufficient for 
a child to be able to spell the words he can use. This view 
is in accordance with the principles of adaptation, 
utihty, and interest. 

Arguments for Text- Book 

256. Convenience. — Time saved for pupil and 
teacher. 

257. System. — Modern books are not miscellaneous 
lists of words; grouping and scope are determined by 
the needs of pupils. 

258. Breadth and utility. — Adequate provision is 
made for future demands as well as for actual present 
use. 

259. Accuracy. — Spelling, syllabication, accent, and 
even pronunciation are accurately given. Errors are 
frequently made in copying lists. 

260. Stimulus. — Ownership is an instinct, and happy 
is the child who is made to feel the worth of such an 
incentive. The average pupil can go far beyond the 
limited list of words in his grade, and a simple appeal 
to personal ambition will encourage him to do so. The 
book is an invitation to self-activity; it is a means to 
helpful rivalry; and it offers individual guidance to the 
future of the child who must leave school to earn a 
living. 

Arguments for Lists of Selected Words 

261. Specific utility. — The words become a part of 
definite knowledge through the child's thinking, feeling, 
and acting. Opposed to vague concepts because the 
child knows and uses every word; development through 
activity and apperception. 



SPELLING 117 

262. Interest. — The child's interest is limited to the 
present; hence, Hmit words to present use. 

263. Adaptation. — Books adapted to average groups 
may not satisfy individual needs. 

264. Economy of effort. — Lists are conducive to 
concentrated, productive effort; books present many 
words that are useless on account of being too easy or 
too difficult. 

265. Correlation. — Lists selected from all the sub- 
jecfs in the grades tend to produce unity and accuracy 
in each child's circle of thought. 

266. Summary of arguments. 

Text-Book List of Words 

General utility Specific utility 

Economy of time Economy of effort 

Provision for future Satisfaction of present needs 

Accuracy of spelling Clearness of concepts 

Adaptation to average Adaptation to individual 

pupils pupils 

Breadth through individual Concentration upon essen- 

effort tials 

267. Combination of book and lists. — Use the best 
text-books available, and then meet the deficiencies of 
the text-book by a list of selected words applicable to the 
individual needs of the class. Combine all useful devices. 

268. Three ways of conducting recitations. — Oral, 
spelling, written spelling, and a combination of oral and 
written spelling are usually classified as three methods. 
Numerous devices are often discussed as methods. 
The three methods mentioned should be combined or 
alternated frequently so that pupils may profit by all 
of the advantages in each method. 



118 METHODS IN EDUCATION 

269. Advantages of oral spelling. 

1. It teaches enunciation, syllabication, pronuncia- 
tion. 

2. Interest stimulated through honest rivalry. 

3. Economy of time by avoiding the necessity of 
correcting papers. 

270. Disadvantages of oral spelling. 

1. It does not insure correct written spelling. 

2. Every pupil does not have to spell all the words 
of the lesson. 

3. Inattention may be fostered in a large class. 

271. Advantages of written spelling. 

1. Practical because it prepares for accurate written 
work. 

2. Every pupil has to spell all the words. 

3. Co-ordination of many senses. 

4. Correlation of many subjects. 

272. Disadvantages of written spelling. 

1. The pupil must use his sense of hearing to obtain 
proper enunciation and pronunciation. 

2. Social stimulus is lacking until the report of the 
exercises is made. 

3. Dishonest work by copying and also in correcting 
the work when papers are interchanged. 

Directions for Studying Spelling Lessons 

273. Physical conditions. — See that the environment 
is satisfactory: hght, heat, ventilation, seats, books, 
and other material. 

274. Responsibility a stimulus. — Prepare the minds 
by telling the children that the purpose of this exercise 
is to master a definite amount of work in a specified 
time. This kind of approach is a compliment to the 



SPELLING 119 

intelligence of the children. There is no harm in using 
the word work since the average healthy child welcomes 
any assignment that carries the possibility of quick mas- 
tery. There is a stimulus in the certainty of success. 
The acceptance of responsibility under hope of success is 
the first victory for the child as the teacher tries to help 
him acquire the habit of vigorous and persistent work. 

275. Concentration. — Have pupils look carefully at 
the word. See sections 241 to 243 inclusive. 

276. Reproduction. — Close book, think of the word, 
write it. Do not permit pupils to try this frequently 
for the purpose of testing themselves. Teach them the 
value of intensive study mentioned in the preceding 
section; then the supplementary use of this reproduc- 
tion will be evident. Observe how this reproduction 
utilizes co-ordination of powers. 

277. Comparison. — Compare the written word with 
the printed word. This is called verification, checking. 
or proving. It is habituation in self-correction, an edu- 
cative effort which Spencer calls empirical. 

278. Repetition. — Repeat the process when mistakes 
have been made. But here is a place to distinguish 
useless repetition and legitimate repetition required in 
fixing habits. While perfection is not expected, every 
pupil should be made to feel the serious waste in 
repeating processes that were first passed over in a 
thoughtless way. The habit of consciously using one's 
powers effectually is the paramount value here as else- 
where. 

279. Rowe quoted. — In support of these suggestions, 
a quotation from Rowe's new book is inserted: ''Four 
habits have usually been formed by the pupil before he 
spells accurately: (1) the habit of critically observing 



120 METHODS IN EDUCATION 

the spelling of new words as he comes upon them in 
reading; (2) the allied habit of noticing where words 
differ slightly from his image or expectation of them; 
(3) the habit of hesitating to write a word whenever its 
spelling may be in doubt; and (4) the habit of taking 
a final glance at the word just written to see that it 
conforms to the intention of the writer and seems cor- 
rect. — Habit-Formation, page 112. 

280. Difficulties. — Meaning of words, use of diction- 
ary, and other pertinent topics relating to the study 
of a spelling lesson are discussed in other parts of this 
chapter. 

281. The old way. — When spelling held equal rank 
with arithmetic and other studies, it was customary for 
the teacher to assign an exercise for study in school or 
at home, and then the pupils considered it a part of 
their duty to learn to spell every word in the exercise. 
This plan of assignment and study is criticised in the new 
education on the ground that the learning of such words 
in that manner is a mere exercise of the memory without 
the use of correlation or multiple sense in the process of 
learning. What, then, shall be substituted? Let us 
interpret some investigations. 

Experiments in Studying Spelling 

282. In Germany. — A German educator, Herman 
Schiller, has made a practical investigation of oral and 
visual modes of learning spelling. His conclusions are 
quoted in Principal W. B. Wait's Annual Report for 
the New York Institution for the Blind, 1903. They 
are in the order of merit, from highest to lowest. 
The quotation marks indicate Mr. Wait's report; the 
comments are ours. 



SPELLING 121 

1. '^Copying with speaking (naming the letters 
softly)." This plan employs the eye, the ear, the tongue, 
and the hand; it requires attention, observation, and 
physical poise; it presupposes good control of the class 
and favorable environment. 

2. '^ Copying with speaking aloud." This plan is 
criticised because the noise made by a large number of 
the pupils may be a source of disturbance to several 
pupils in the class. 

3. '^Seeing with writing movements." Lender this 
plan a word is written on the blackboard or on a card 
so that every pupil in the class can see it. Pupils vis- 
ualize the word. In making the writing movements in 
the air, their effort to learn combines the sense of sight 
and the motor activity. 

4. ''Spelling (hearing the letters named)." This 
plan is criticised because it deals with letters as the 
units of our language instead of considering words as 
symbols of ideas. 

5. "Seeing with speaking aloud." 

6. "Seeing with speaking softly." 

7. "Seeing alone." 

8. "Hearing with writing movements." 

9. "Hearing and speaking aloud." 

10. "Hearing with speaking softly." 

11. "Hearing alone (word pronounced only)." 

"In all these methods, except hearing the letters 
named, and hearing the word pronounced, but not 
spelled, the work is done by the pupil alone. Spelling 
based upon words pronounced but not spelled to the 
pupil takes the lowest place, but spelling based on words 
both pronounced and spelled to the ear takes fourth 
place. Here it should be noticed that there is a long 



122 METHODS IN EDUCATION 

period in the child's hfe before it has learned to read or 
write, when hearing and speech are the only available 
means of learning language." 

''It will be seen that Schiller gives first place to a 
composite method, copying and speaking softly; the 
complete act involving the four memories, namely, a 
visual form of memory, a manual motor memory, vocal 
motor memory, and the aural memory." 

283. Suggestions to the teacher. 

1. Pronounce the word only once. 

2. Give only one trial in oral spelling. 

3. Work for natural tones in spelling. 

4. Do not mispronounce unusual words for the sake 
of aiding the child in spelhng such words. 

5. Vary the order from that given in the spelhng book. 

6. Have pupils pronounce the word before and after 
spelling it. 

7. Have children pause at the end of each syllable, 
but do not have them pronounce each syllable separately. 

8. Teach phonic spelling whenever that will be an 
aid in mastering the words. 

284. Rules for spelling. — A few simple rules may be 
helpful to pupils who find difficulty in ordinary spelling, 
but such memorizing should be limited to actual useful- 
ness. The limitations are evident as soon as a child 
finds more difficulty in learning and applying the rules 
than in memorizing the words themselves. 

The substance of the rules is the same in all texts, 
but simplicity and clearness in wording is found in the 
following from Reed and Kellogg's Higher Lessons in 
English, page 258. 

Rule I. — Final e is dropped before a suffix beginning 
with a vowel; as, fine, finer, love, loving. 



SPELLING 123 

Exceptions. — The e is retained (1) after c and g 
when the suffix begins with a or o; as, peaceable, change- 
able; (2) after o; as, hoeing; and (3) when it is needed 
to preserve the identity of the word; as, singeing, dyeing. 

Rule II. — Y after a consonant becomes i before a 
suffix not beginning with i; as, witty, wittier, dry, drier. 

Exceptions. — Y does not change before 's, nor in 
forming the plural of proper nouns; as, lady's, the Marys, 
the Henrys. 

fiule III. — In monosyllables and words accented 
on the last syllable, a final consonant after a single vowel 
doubles before a suffix beginning with a vowel; as, hot, 
hotter; begin, beginning. 

Exception. — X, k, and v are never doubled, and gas 
has gases in the plural. 

285. Classification of words. 

1. Primitive. A word in its simplest form is a prim- 
itive or prime word; as, by, in, man, short, go. 

2. Derivative. A word formed from a primitive 
word by joining prefixes or suffixes is a derivative word; 
as, going, unmanly, recall. 

3. Compound. Two or more words united into one 
word form a compound word; as, today, watchman, 
subject-matter, text-book. 

4. Synonyms. Words having the same or similar 
meaning are synonyms; as, hope and expect; certain 
and sure; devout and pious. 

5. Antonyms. Words having opposite meaning are 
antonyms; as, good and evil; lazy and industrious. 

6. Homophones. Words having the same sound but 
different spelling and meaning are homophones; as, 
sell and cell; beer and bier; write, rite, and right. Some- 
times called paronyms or homonyms. 



124 METHODS IN EDUCATION 

7. Homonyms. Words having the same sound and 
spelling but different meaning are homonyms; as the 
verb bear and the noun bear; the verb receipt and the 
noun receipt. Sometimes called homographs. 

286. How to teach synonyms. — The first attention 
to synonyms will be directed by the teacher. During 
the class criticism of compositions, favorable occasions 
will arise. The teacher's explanation must be the 
source of information until pupils are able to under- 
stand the dictionary distinctions. Pupils enjoy the 
liberty of expression that seems to be granted by the 
choice of words. Following are suggestions: 

1. Let oral and written language show the need of 
synonyms. 

2. The early use of synonyms is larger power of 
expression; a later use is precision in language. 

3. Observe the choice of words in quotations, dicta- 
tion, and other literary material. This is using a model. 

4. Have pupils use their own language in making 
distinctions; verify answers by dictionary or other 
authority; use the synonyms in sentences. 

Illustrations 

1. Ability, capacity. Ability is active power; capac- 
ity is receptive power. You have shown ability in 
algebra and capacity in literature. 

2. Between, among. Between is a preposition show- 
ing relation of two things; among, more than two. 
Rachel stood between first and third among forty pupils. 

3. Character, reputation. Character is what you 
are; reputation is what people think you are. ''Char- 
acter is injured by temptations and by wrongdoing; 
reputation by slanders and libels." 



SPELLING 125 

4. Compare, contrast. Compare is to find resem- 
blances; contrast, to find differences. Compare Labra- 
dor and England in latitude and contrast them in 
climate. 

Habit, custom, usage. Habit relates to acts of an 
individual; custom implies the consent of many; usage 
is established custom. If you wish to conform to the 
usage of literary men, observe the custom of our best 
writers and then try to form habits accordingly. 

A Lesson on Synonyms 

Aim. To teach the synonyms habit, custom, usage. 

Preparation. The teacher has directed the atten- 
tion of the pupils to synonyms in the correction of com- 
positions. Models in Hterature have been studied for 
the purpose of observing choice and distinction of words. 
Synonyms in reading lessons have been explained and 
discussed. Now the pupils are prepared to note the 
differences in meaning in these synonyms: habit, cus- 
tom, usage. 

Three sets of sentences are written on the board: 

Set I 

1. John has the habit of arising at six every morning. 

2. Mary's habit is to practice every afternoon. 

3. Rover has the habit of watching for his young 
master every afternoon. 

4. Lincoln formed the habit of collecting and telling 

amusing stories. 

Set II 

1. It is the custom of factories to close at five o'clock. 

2. The custom of our school is to have assembly 
every morning. 



126 METHODS IN EDUCATION 

3. It is the custom of the boys to subscribe to Current 
Events every term. 

4. The Chinese customs do not differ from those of 
their ancestors. 

5. It is the custom of the American people to honor 
the anniversary of Lincoln's birthday. 

Set III 

1. Usage demands that February 12th be celebrated 
with appropriate pubHc exercises. 

2. The usage of the best writers calls for simple, 
direct English. 

3. The usage of the Chinese has prevented the intro- 
duction of western ideas. 

4. Usage demands that men remove their hats on 
entering church. 

Presentation. The sentences containing the word 
habit are read by several pupils. Then the teacher 
conducts the lesson by questioning. Brief answers are 
suggested here, but answers in complete statements 
may be required in the lesson with the class. 

Teacher. How many people are spoken of in the 
first sentence? 

Pupil. One. 

Teacher. What habit has he? 

Pupil. The habit of arising at six. 

Teacher. How often has he arisen at six? 

Pupil. Every morning. 

Teacher. Does this action require effort and think- 
ing? 

Pupil. No. 

Teacher. Why? 

Pupil. He has done it so often it is easy now. 



SPELLING 127 

Teacher. What have we called Mary's act of prac- 
ticing, in sentence two? 

Pupil. A habit. 

Teacher. In each sentence we have spoken of how 
many people? 

Pupil. One. 

Teacher. What have we called the action of each? 

Pupil. A habit. 

Teacher. Habit is used, then, in relation to how 
many people? 

Pupil. One. 

Many pupils are called upon to state: Habit is used 
in relation to the acts of one person. 

Set II. On Custom 

Teacher. Does the fifth sentence refer to one or more 
than one? 

Pupil. To more than one. 

Teacher. What does that sentence say the people 
do? . 

Pupil. Honor the anniversary of Lincoln's birthday. 

Teacher. What is the action called? 

Pupil. A custom. 

Teacher. Why did the United States form the cus- 
tom of honoring Lincoln's birthday? 

Pupil. Because the people loved him and wished 
to show their gratitude to him. 

Teacher. They all agreed, then, to the act of honor- 
ing his birthday. That agreement of many people 
made the honoring of Lincoln a custom. 

Similar procedure with the other sentences in Set II. 

Teacher. Look at the sentences in Set II again. Do 
you think a few people can make a custom? 



128 METHODS IN EDUCATION 

Pupil. No; custom requires the agreement of a 
large number of people. 

Teacher. Custom implies the consent of many, as 

you have said. This conclusion is expressed by several 

pupils. 

^ ^ Set III. On Usage 

Teacher. What demands that February 12th be 
celebrated with appropriate pubhc exercises? 

Pupil. Usage. 

Similar procedure with other sentences in Set III. 

Teacher. How was Lincoln regarded by his country? 

Pupil. He was regarded as a hero whom all loved. 

Teacher. According to the first sentence, how may 
we honor our heroes? 

Pupil. By celebrating their birthdays. 

Teacher. How long has this custom been observed? 

Pupil. A very long time. The people of the olden 
times did likewise. ' 

Teacher. A custom that has lived very long becomes 
usage. It is accepted and followed by the best thinkers. 

Teacher. What does usage or long established cus- 
tom ask of good writers of English? 

Pupil. Simple, direct language. 

Comparison. One sentence in each group is consid- 
ered. All three are compared and the differences in 
meaning brought out. Children state in their own 
words the distinction. Pupils are sent to dictionaries 
to verify the distinction in use. 

Application. The teacher requires the children to 
give sentences employing the synonyms. 

Sentences with blanks are written on the boards. 
The pupils fill in the blanks with the proper synonyms, 
always stating why they have used the synonyms chosen. 



SPELLING 129 

Teacher encourages the use of the synonyms learned 
in oral and written work. 

287. How to teach homophones. — As these words 
are ahke in sound, the sense of hearing alone will lead 
to error. Observe the difference in spelling and the 
difference in meaning. With younger pupils, the words 
should be mastered one at a time; with older pupils, the 
whole group furnishes a basis for contrast and a stimulus 
for mastery. A few groups will suffice. It is under- 
sfbod, of course, that use in good sentences is one final 
test of a knowledge of the spelling and the meaning of 
homophones. The Rational Spelling Book, by Dr. J. M. 
Rice, calls such words as these homonyms : 

bad, wicked rite, a ceremony 

bade, did bid right, correct 

write, to record letters 
dying, expiring wright, a workman, 

dyeing, coloring 

air, atmosphere 

rain, water from clouds ere, before 
reign, to rule e'er, ever 

rein, part of harness heir, one who inherits 

Ayr, a town in Scotland 

288. How to teach homonyms. — Since homonyms 
differ in meaning only, this one difference is the point 
to attack in teaching and learning. Recall all that has 
been approved as efficient teaching of spelling and apply 
as much of it as possible in teaching homonyms. Here 
are a few specific directions: 

1. Teach only such homonyms as young children 
need to know. 

2. Teach one homonym at a time. 



130 METHODS IN EDUCATION 

3. Teach by conversation and explanation ; have pupils 
converse, explain, and use the word; write sentences. 

4. Teach the corresponding homonym in a similar 
manner. 

5. Use both in sentences; drill on meaning and spell- 
ing; pupils construct sentences. 

6. Illustrations of homonyms. 

bear, an animal 
bear, to carry 

cheer, good feeling 
cheer, to encourage 

saw, a carpenter's tool 
saw, did see 

How to Teach the Meaning of Words 

289. Associative or objective process. — The object 
is shown and the name applied. If object cannot be 
used, show picture or other representation such as a 
drawing. Moulding board is a familiar means. Thus 
in teaching the noun divide, a word used for watershed 
in geography. Observe a divide in the school yard 
after a rain; compare roof; make an excursion to a hill 
and see that it is a divide; use pictures, drawings, and 
sand table. 

290. By imitation. — Buzzing, flying, swimming, row- 
ing, and similar words are represented by action; likewise 
for words like mew, bark, purr, neigh, and bleat. This 
activity appeals to the dramatic instinct in children. 
Compare kindergarten activity. 

291. By the context. — Most words being under- 
stood, focus attention upon what is not understood and 
then try to supply or substitute the meaning needed 



SPELLING 131 

to complete the thought in the sentence. Take a quo- 
tation from Hawthorne: ''Happiness in this world, 
when it comes, comes incidentally. Make it an object 
of pursuit, and it leads us a wild-goose chase, and is 
never attained." The itahcized words can be defined 
from the context. 

292. By etymology. — Take autograph: graph, write; 
auto, self; a signature written by the person himself. 
Compare telegraphy, phonograph, geography, stenog- 
raphy. 

Consult Anderson's ''A Study of English Words," 
American Book Company, 1897; Trench's " On the Study 
of Words"; Greenough and Kittredge's ''Words and their 
Ways in Enghsh Speech," Macmillan, 1901; Kennedy's 
"What Words Say." 

In analysis and synthesis pupils should use the tech- 
nical names of parts of words. Root, stem, base, ad- 
junct, prefix, and suffix are used by different authors, 
but base, prefix, and suffix are enough. 

The primitive form of a word is the root. It is the 
name used by philologists to denote the original form 
and meaning of the word. 

That part of a word to which the inflectional endings 
are added is the stem. The stem may be the same as 
the root, or it may be a modified form of the root. Thus 
in abduct, due is the root; duct is the stem. 

The word or stem to which other parts are joined is 
the base. The base may be a word, as in man + hood; 
or it may be a stem, as in auto + graph. 

A form or word joined to the base is an adjunct; as, 
rest + ful, steam + boat. 

A form placed before the base is a prefix; after the base 
a suffix. 



132 



METHODS IN EDUCATION 



ILLUSTRATIONS 



PREFIX 

ad, to 

bene, well or 
good 

contra, . 
against 

super, above 



ob, against 



BASE 


SUFFIX 


DERIVATIVES 


MEANING 


join, add 




adjoin 


to join to 


factor, doer 




benefactor 


one who does good 


diet, speak 




contradict 


to speak against 


script. 


ion, that 


super- 


that which is written 


written 


which 


scription 


above 


vi, way 


ous, being 


obvious 


being directly in the 
way, against or in 
front of us 


ject, 


ive, in- 


adjective 


inclined to be thrown 


thrown 


clined to 




to another word 



ad, to 



293. By the history of words. — This is another kind 
of etymology. Thus dahha is derived from the name 
of the botanist Dahl. Dunce is from Duns Scotus, a 
famous scholar, whose theories were later ridiculed so 
much that his name became a synonym for stupidity. 
Trivial is from tres viae, the junction of three roads in 
Rome where gossipers spent their time in idle talk. 
Sincere is sine, without, and cera, wax; a guaranty 
applied to perfect vases sold in Italy. 

294. By finding synonyms. — Comparison and con- 
trast impresses the meaning and at the same time 
enlarges the vocabulary. For example, take excite and 
incite. Excite, to rouse feelings for action; incite, to 
urge the excited feehngs to accomphsh something. A 
teacher excites her pupils for the consideration of social 
duty and then incites them to do their duty. 



SPELLING 133 

295. How pupils may show their knowledge of the 
meaning of words. 

1. By the use of the words in conversation. 

2. By interpretation of the words in reading. 

3. By constructing illustrative sentences. Inflam- 
mable means burning with a flame, while combustible 
means burning without a flame. 

4. By forming definitions. 

5. By using synonyms. 
d. By giving etymology. 

7. By drawings and models. 

296. Means of learning pronunciation. 

1. By imitation of teacher. 

2. By phonic drill. 

3. By practice under 295. 

297. Uses of the dictionary. — The dictionary is 
intended as a means of verification and also as a source 
of general information. Facility of use of the diction- 
ary implies the following: 

1. How to find the word. 

2. How to understand the sounds of the letters as 
indicated by the diacritical marks. 

3. Mastery of syllabication. 

4. Observation of accent. 

5. Pronunciation. 

6. In the higher grades, discrimination in the use of 
words, etymology, etc. 

298. Devices in word-building. — This synthetic drill 
supplements the exercises in analysis of words, and also 
serves as generalization and appHcation of all phases 
of knowledge in spelling. 

1. Write on the board a dozen prefixes with meanings, 
root-words, and sufl&xes. Help the pupils memorize 



134 METHODS IN EDUCATION 

these three lists, and encourage pupils to add other pre- 
fixes, roots, and suffixes. Copy lists in books for perma- 
nent use at home or in school. This material can be 
used in a lively competition to form the largest number 
of words. Pupils should consult dictionary to prove 
the accuracy of their own work. For helpful reference 
books, see section 292. 

2. Each pupil gives a word having the suffix er, and 
then defines the word. 

3. One pupil gives a word and another pupil names 
synonym or homonym. 

4. Teacher suggests a word like graphic; pupils give 
other words having the same root. 

5. Suggest phonogram such as ail; conduct phonic 
drill on b, f, h, j, m, n, p, qu, r, s, t, w; combine; spell 
phonetically; use in sentences. Proceed in a similar 
manner with other phonograms like ate, at, et, air, ow. 
All the letters of the alphabet will thus receive phonic 
drill. 

6. Form words from letters. Grant right to use the 
whole alphabet, but put a time limit upon the work. 
This exercise is a test in the constructive ability of the 
pupil. It is the synthetic process of testing analysis. 
Every effort to form a word from the given letters makes 
an exercise in recalling the roots, the prefixes, and the 
suffixes in familiar words. At the same time it may be 
a review of phonics as employed in homonyms and anto- 
nyms. 

299. Grouping words by comparison. — We have 
already said that grouping words according to the number 
of syllables is unscientific. Some authors group accord- 
ing to meaning; others according to subjects or occupa- 
tions. Comparison in spelling looks for similarities. 





SPELLING 




out 


ought 


rough 


hour 


thought 


enough 


drought 


sought 


tough 


pout 


bought 


slough 


stout 


brought 


southern 


dough 


through 


should 


soul 


wound 


would 


source 


tour 


could 


shoulder 


you 




although 







135 



300. Grouping by contrast. 

hour bow nought too 

power sew naught through 

rough wood dough 

ruff should low 

301. Correlation through dictation. — The dictation 
exercises made by the teacher or the pupils will use the 
related parts of the grade work. If the pupils are fol- 
lowing a selected list of words instead of a spelling book, 
it is likely that every word is studied in its related sense 
rather than as an isolated word. The summarizing 
value of adapted dictation exercises includes the correct 
use of the assigned words, the words misspelled from 
time to time, the words considered essential in the assign- 
ment of other lessons, and, in general, whatever words 
are needed in making the transition to a new grade by 
promotion. If this summary seems too comprehensive, 
it is justified by the requirements of the pupils' daily 
experience. The habit of accuracy in written work and 
the breadth of content secured by correlation make 
dictation exercises a direct preparation for life. 



136 METHODS IN EDUCATION 

302. "Make every lesson a spelling lesson." — Not 
approved pedagogy. The custom of directing atten- 
tion to misspelled words in every recitation is likely to 
distract the pupils l>y taking their attention from con- 
nected thinking in some other line of work. Such dis- 
traction cannot be justified for the sake of correcting 
misspelled words. As already suggested, there should 
be a special spelling list in every class. It is better for 
the teacher to make note of any errors in the other 
lessons and then reserve those misspelled words for 
the regular exercise during the spelling period. 

303. Pronunciation of each syllable. — This practice 
is not generally approved. It is better to indicate a 
syllable by a pause, since the pronunciation of each syl- 
lable tends to separate the word into too many elements 
and thus to destroy its function as a symbol of one idea. 

304. Repetition in writing misspelled words. — Do 
you approve writing misspelled words fifty times or 
more? No, not even ten times. Such an exercise is 
harmful as a means of correction. After a number of 
repetitions, the writing becomes a formal exercise with- 
out thought. 

Variety in the Recitations 

305. Combination plan. — Teacher pronounces words, 
pupils write on paper; teacher spells words, each pupil 
marks his own paper and rewrites misspelled words. 
Oral spelling of all the misspelled words. This plan 
maintains order, institutes the habit of systematic pro- 
cedure and requires the use of self-activity and individ- 
ual responsibility. It is a preparation for future pupil 
government in the spelling period. 

306. Self-correction. — Teacher pronounces words, 



SPELLING 137 

pupils write; self-correction, pupils consulting books; 
papers submitted to teacher. This plan is an effort 
toward self-correction and a test of observation, indus- 
try, and honesty. The pupil does the work. 

307. Interchange. — Teacher pronounces words, 
pupils write; papers exchanged, marked, and returned; 
critics consult each other if necessary and refer to books 
to settle disputes. Such mutual criticism exalts the 
function of criticism, habituates the critic in accuracy, 
ha's justification by authority, and gives the conscious- 
ness of social responsibility. Each pupil begins to feel 
his twofold duty to the class and to himself. 

308. Monitor. — Teacher pronounces words, pupils 
write; one pupil stands, faces class, pronounces and spells 
while the others mark their own papers. Replace the 
spelling monitor if he misspells a word. This device 
tests enunciation, syllabication, and pronunciation; 
stimulates the desire of recognized leadership; promotes 
an active class spirit, and sustains a healthy interest 
in the work of the recitation period. 

309. Group criticism. — Divide the class into two 
groups; all pass to the board; one group writes, the other 
group criticises; teacher or pupil pronounces words. 
Alternate the groups. In this way the teacher sees all 
the work and readily estimates its accuracy while the 
pupils are actually doing the work. 

310. Individual responsibility. — One group at board, 
one group writing at desks. Teacher pronounces words, 
notices errors at the board, and pronounces a second 
time the misspelled words. Pupils at seats aid as critics. 
This exercise is an economy of time for teacher and pupil 
as it serves to approximate the work of a regular exam- 
ination. 



138 METHODS IN EDUCATION 

311. Class responsibility. — Appoint a committee of 
five pupils to prepare words for one week. Let this 
committee put words on board, conduct spelling reci- 
tation, mark papers,^ tabulate reports, and suggest 
remedies for faults. This plan has so many merits 
that none but a weak teacher will reject it. 

312. Alertness. — All stand, spell in order, teacher 
not mentioning the misspelled words. The pupil who 
detects and corrects a misspelled word passes to a place 
of honor. This utilizes the competitive instinct in chil- 
dren and promotes the habit of thoughtful alertness. 

313. Choosing sides. — Group instinct, loyalty, deter- 
mination to win. 

314. Spelling down. — Individual satisfaction in vic- 
tory after honest rivalry. 

Co-operation through Responsibility 

315. Pupils as examiners. — Ask the pupils to 
prepare twenty-five words for spelling examination. 
Suggest that this work be done at home so that the 
individual element may be sure to be felt. 

316. Pupils as reviewers. — Invite pupils to make 
dictation exercises covering the work of a week or a 
month. Insist upon the standard of accuracy in spell- 
ing, capitalization, and the proper use of the words. 
Invite the use of sentences taken from literature or some 
other subject in the grade rather than the construction 
of sentences dealing with meaningless thoughts of the 
child. 

317. Pupils as critics. — Assign one pupil as leader 
with the privilege of choosing four others to serve with 
him as critics in marking the class exercises for a certain 
day. Have the work done at home and have each critic 



SPELLING 139 

sign his name to the paper marked by him. Return 
papers the following morning and distribute them to 
their owners. Give each pupil the right of appeal to 
his critic and finally to the teacher. This exercise 
emphasizes the responsibility of the critic while it teaches 
the child the real meaning of criticism as distinguished 
from fault-finding. 

318. Pupils as friends. — Suggest the desirability of 
trying to attain the teacher's ideal of neatness and accu- 
racy. This appeal from a true teacher will secure the 
desired response. 



CHAPTER X 
COMPOSITION 

319. Utility and culture. — To him who looks for the 
practical value of education, oral and written composi- 
tion has recognized usefulness as a means of business 
intercourse. No argument is needed to justify the 
prominence given to composition in the course of study; 
the only appeal is for some kind of teaching that shall 
assure rapidity and accuracy in the approved forms of 
commercial expression. 

There is another value in composition, aside from that 
which helps to earn a living. It is the culture value. 
Literature is composition; and out of the treasures of 
literature many a mind has drawn a compensation that 
is not measured by dollars and cents. It is a compensa- 
tion that serves as a satisfactory substitute for much 
that is lacking in life. This joy of literary appreciation 
is a direct stimulus to imitative construction in composi- 
tion. Here is one reason why pupils are required to 
study literary masterpieces as models. In studying a 
type of composition, the pupils are getting proper habits 
of interpretation and appreciation; the appreciation 
arouses a desire to imitate; and the desire to imitate is 
carried into execution through the voluntary act of the 
will. Thus we have an educational process in which 
the fruitage of culture is both a cause and an effect. 

320. General aims. 

1. To educate by stimulating thought. 

140 



COMPOSITION 141 

2. To develop the habit of fluent, easy, and correct 
expression. 

3. To help impression through expression. 

321. The pupils' motives; pleasure, spontaneity, in- 
terest. — To relieve the writing of compositions from all 
feelings of drudgery, teachers are urged to make the 
desire of giving pleasure the predominating motive of 
the child. As soon as a pupil aims to write something 
that will please his teacher or his classmates, or any 
other friends, his production will be characterized by 
spontaneity; in reading it or having it read, his interest 
will be sustained or increased; and after receiving favor- 
able criticisms, which should always be given, he has a 
powerful stimulus for more and better work in this line. 
Note that the intellect, the feelings, and the will are all 
strengthened as the pupil habituates himself to writing 
under these conditions. 

322. Principles determining selection of matter for 
compositions. 

1. Within scope of child's knowledge. 

2. Within scope of child's interest. 

3. Limited to prevent wandering. 

If we assume that grading satisfies the welfare of the 
pupils, we may conclude that these principles apply 
whenever a theme for composition is selected within the 
prescribed limits of the grade work. In the fourth 
grade, for instance, is the theme Columbus a satisfac- 
tory theme? Under principle one, it should be satis- 
factory; under principle two, it is satisfactory; but under 
the third principle, it must be rejected. But limit the 
thought to The Boyhood of Columbus, and we have a 
theme that satisfies the three principles. Test in the 
same way for the seventh grade. The theme Columbus 



142 METHODS IN EDUCATION 

presents even more danger of scattering thoughts; but 
choose The Discovery of Land for a descriptive com- 
position, and there will be no need of depending upon 
text-book theory for the valid application of the three 
principles mentioned. 

As another illustration, take The Panama Canal. 
Is it, as a subject, topic, or theme for elementary grades, 
justifiable? It is or can be within the realm of interest 
of every child above the third grade, but has the average 
pupil enough definite knowledge for serviceable exposi- 
tion? Probably not; and, for this reason, the third 
principle is not satisfied. But it is possible to limit the 
scope of this subject, get the desired information, and 
then write a composition in accordance with the prin- 
ciples stated, or any other principles accepted for the 
guidance of the work in composition. 

The experienced teacher passes quickly from abstract 
principles to test the results of classroom work. Theo- 
retical tests must yield to practical tests. The good 
teacher makes the subject conform to accepted prin- 
ciples because she knows the interrelation of knowledge 
and interest. Having these two, she makes the writ- 
ing of the composition a pleasurable reaction. Thus 
the three principles are exemphfied in one teaching 
act. 

323. Suggestions for the teacher. — Much help can 
be found in Carpenter, Baker, and Scott's The Teaching 
of English. See page 134, in support of these sugges- 
tions on the preparation of the teacher: 

1. Choose a subject that has possibilities; keep in 
mind the principles given in section 337. 

2. Present it in such a way as to make the pupils 
see its possibilities. 



COMPOSITION 143 

3. Stimulate oral discussion, but so direct it as to 
prevent wandering. 

324. Kinds of composition exercises. — The two gen- 
eral divisions of composition work are oral and written. 
Under each of these there are various subordinate kinds 
which will be discussed in this chapter. One mistake 
in teaching is to separate oral and written exercises. 
Each aids the other and both should be used in every 
development exercise. 

' 325. Oral composition. — This form of composition 
naturally precedes written composition, but pupils do 
not realize that talking is composing. While oral com- 
position is a specific kind in itself, it should always 
be used as a preliminary preparation for every written 
composition. It makes the transition easier because the 
pupil feels that the writing is only another way of express- 
ing what has already been expressed orally. 

■ 326. In primary grades. — In the lower primary 
grades, the oral work may be divided into conversation 
and reproduction, the aim of the latter being to have 
the child give the exact words as nearly as he can. 
Simple and interesting conversation topics may include 
nature study, pictures, experiences of childhood, facts 
impressing kindness, good conduct, cleanhness, and 
courtesy; and a little later the use of myths, fables, and 
historical narratives may be introduced. 

327. Dr. Maxwell on oral composition. — The phases 
of oral composition are here presented in seven headings, 
as originally printed in School Work, Volume I, page 1. 
In regard to the use of sentences to explain the meaning, 
some recent writers do not agree with Dr. Maxwell's 
opinion in number 7 below. They hold that correct use 
in a sentence is a serviceable way to teach the meaning 
of words. Compare section 295, 



144 METHODS IN EDUCATION 

Kinds of Oral Composition 

1. All answers to questions should be given in com- 
plete statements. 

2. Discussion of the contents of the reading lesson. 

3. Reproduction of stories told or read by the teacher. 

4. Description of processes in arithmetic and manual 
training. 

5. Separation of sentences into their complete sub- 
jects and predicates. 

6. Recitation of prose and poetry. 

7. Explanation of the meaning of words. Putting 
words into sentences is not a method of teaching the 
meaning of words, but a method of determining whether 
the meaning of a word is known. 

Kinds of Written Exercises 

328. Optional classification. — Some kinds of written 
work are suggested here, but other classifications are 
accepted. Teachers will see the necessity of using oral 
work in connection with transcription, dictation, forms 
of correct expression, reproduction, paraphrase, abstract, 
and elaboration. 

329. Transcription or copying. — Much importance is 
placed upon the habit of copying correctly from the 
board, paper, or books. Very few advanced pupils are 
able to copy accurately, because they never formed the 
habit of doing so in the primary grades. This exercise 
may be directed so as to teach or review capitalization, 
punctuation, unity of the sentence, sequence of thought, 
and paragraphing. Select material that is interesting 
and intelligible, and then require absolute accuracy. 
Do not make these exercises too long or too frequent. 



COMPOSITION 145 

330. Dictation. — Exercises in dictation have a wide 
use in applying the principles of composition, and espe- 
cially in forceful drilling to correct errors. Dictation 
exercises teach the child to put on paper what is in his 
mind, thus helping to make the transition from spoken 
to written language. Use exercises having ethical or 
literary content. If the exercises for dictation are taken 
from the books used by the pupils, self-criticism is made 
easy and practical. 
' 331. Forms of expression. — Exercises on correct 
forms of expression will habituate the pupils to the 
proper use of words before the technical reasons are 
understood. It is a good plan to devote at least five 
minutes a day to oral exercises of this nature. Repeat 
the essential exercises day after day until the form sounds 
right to the children. Remember that it is the ear that 
gives us most of our habits of speech. Only oral repeti- 
tion will fix the correct habits. Keep a list of the errors 
frequently made, and then arrange the dictation exer- 
cises accordingly. These exercises include such words 
as is and are, have and had, doesnH and donH, shall and 
will, may and can, double negatives, and other common 
errors. 

332. Reproduction. — This form of composition exer- 
cise means the recalling of the exact words of the author. 
This restricted meaning of reproduction may not be 
accepted outside of New York City. Here and else- 
where the selections for reproduction should be models 
in thought and style. 

333. Paraphrase. — This exercise means the expres- 
sion of another's thought in one's own language. It is 
helpful in causing a pupil to get the thought expressed 
in a given passage; but many educators consider it a 



146 METHODS IN EDUCATION 

harmful exercise because it degrades the author's beauty 
of style and thought. Better to memorize the selec- 
tions for reproduction. 

334. Abstract. — A condensed statement of the sub- 
stance of another's thought in one's own language is an 
abstract. 

335. Elaboration. — This term is the converse of 
abstract writing. Brevity characterizes the abstract; en- 
largement and elucidation are characteristic of elabora- 
tion. It is an exercise conducive to freedom of thought 
and expression in narration, description, and exposition. 

336. Kinds of written composition. — Description, 
narration, and exposition are three kinds used in ele- 
mentary classes. Description presents the appearance 
of things; narration presents a series of actions or hap- 
penings; while exposition seeks to explain the meaning 
of things. For a satisfactory treatment of how to teach 
these and other kinds of elementary composition, see 
Maxwell and Johnston's School Composition, or any 
other good text. 

337. Problems. — The difficulties or problems in 
teaching composition may be summarized as follows: 

1. The selection of subjects, topics, or themes. 

2. How to conduct the recitation preparatory to 
writing. 

3. Criticism and correction. 

4. The use of models in 1, 2, 3. 

338. Selection of subjects. — Three considerations are 
sufficient. 

1. Principles. Same as in section 322. 

2. Correlation. Select subjects from history, geog- 
raphy, and other grade work. This kind of selection 
comes under the principles in 1. 



COMPOSITION 147 

3. Avoid such abstract subjects as Vanity, Ambition, 
The Growth of Pessimism. This suggestion is also 
under the principles in 1. Teachers are frequently asked 
for a positive suggestion on the selection of subjects, and 
so 2 is given; for negative suggestion, use 3. 

339. Some suitable subjects. 

FOURTH YEAR 

Science. Coal and Its Uses. 
' Geography. The Harbor of New York.\ 
History. Henry Hudson. 
Biography. Longfellow. 
Personal experience. A Visit to the Museum. 

FIFTH YEAR 

Subjects similar to those in Fourth Year. 
Narrative. The Boyhood of Lincoln. 
Descriptive. The Making of a Base Ball. 

SIXTH YEAR 

Advantages of the Panama Canal. 

The Aunt in Snow Bound. 

Why I Like Whittier. 

The Necessity of Bathing. 

What I Should Do with a Thousand Dollars. 

The History of Our Flag. 

SEVENTH YEAR 

Narration. My Progress in Four Years. 
Description of a picture. The Signing of the Declara- 
tion of Independence. 

Exposition. The Uses of Our Forests. 



148 METHODS IN EDUCATION 

Argumentation. Virginia vs. Massachusetts in Amer- 
ican Progress. 

Science. Wireless Telegraphy. 

History. The Decisive Effect of the Battle of Sara- 
toga. 

Geography, History, and Literature in Evangeline. 

EIGHTH YEAR 

My Favorite Character in the Deserted Village. 

The Kinds of Levers. 

My Opinion of Webster as an Orator. 

The Power of Simple Words in the Gettysburg Speech. 

The Causes of the Mexican War. 

340. The model as a preparation for writing. — See 
specific directions in School Composition. We shall pre- 
pare the class for writing by studying, analyzing, and 
imitating a model. Another exercise will deal with the 
preparation of original material. 

341. The selection of a model. 

1. Select a model from some book in the class. Every 
pupil should have a copy in his hand. Why? See last 
two sections in geography. 

2. Select a model that the class will appreciate. There 
can be no culture value in interpretation that lacks 
appreciation. 

3. Select a model having some rhetorical excellence, 
such as clearness, choice of words, or good outline. 

342. The study of the model. — Suppose the model 
selected is The American Indians, a prose selection in 
the class reading books. 

1. Pupils read selection to get the general nature of 
the selection. 

2. Second reading for the more careful treatment of 



COMPOSITION 149 

important parts, the aim being to bring about an appre- 
ciation of the beauty of the selection rather than to 
accumulate a fund of information concerning words or 
allusions. But there is special attention given to what 
words are used and how they are used; to structure, 
capitalization, and punctuation of sentences; to unity, 
continuity, and topic sentence in each paragraph. This 
analytic study reveals the structure of the parts and the 
whole, and also enables the class to make an outline 
skowing the thought or plan of the author. 

3. A third reading will give increased appreciation 
and leave the selection as a unit in the pupils' minds. 

343. Imitation of the model. — The study of the 
model gave as an outUne. It shows the thought in the 
author's mind and the arrangement or plan in the selec- 
tion. It follows: 

THE AMERICAN INDIANS 

I. Introduction. Probable origin of the Indian 
race. 

11. Body. 

1. Physical appearance and dress. 

2. Manner of living; occupations, pleasures. 

3. Relation to the white people, as friend and as 
enemy. 

4. Future of the Indians. 

III. Conclusion. A peculiar type of man in Ameri- 
can life. 

Now have the pupils give the substance of the selec- 
tion, using their own oral wording. 

Observe outhne again. Take The Eskimo for a sub- 
ject and write a composition according to this same 
outline. A kindred subject is considered better than 



150 METHODS IN EDUCATION 

the same subject, as the latter invites too much use of 
verbal memory. 

344. The model in criticism. — Now the compositions 
on The Eskimo are ready for criticism, supposing that a 
day or more has elapsed since the compositions were 
WTitten. Comparison with the model is the process; 
and the points to be observed are the ones observed in 
the study of the model. This first criticism by com- 
parison should be done by teacher and pupils working 
together. 

345. Outlines. — The study of the paragraph leads 
to the use of outlines. In the fourth grade the teacher 
should co-operate with pupils in making outlines and 
then have pupils compose orally on these outlines before 
writing. Some hold that this making of outlines pro- 
duces mechanical, uninteresting, and unimaginative 
writing; but, on the other hand, the weight of opinion 
favors the plan as a means of securing unity and con- 
tinuity of thought. 

346. Purposes of outlines. 

1. To aid in the gathering of material. 

2. To secure its proper organization and condensation. 

3. To secure the logical order of topics. 

4. To leave the mind of the writer free for the expres- 
sion of his ideas. 

5. To prevent wandering. 

6. To fix the habit of clear, logical thinking. 

347. Composition without model. — The time will 
come, of course, when pupils will write compositions 
without using a model as a preliminary preparation. 
The model is only a type, and so the model is not re- 
quired after the type has become familiar. In such 
cases, a regular order of procedure may be used. 



COMPOSITION 151 

1. Assignment of theme. 

2. Books should be read, lessons reviewed, subjects 
investigated; in short, information gathered from all 
convenient sources. 

3. Oral discussion for summarizing, condensing, and 
organizing material. 

4. Write outline. 

5. Oral composition following outline. This may be 
omitted in the higher grades. 

-6. Write composition. 

348. Criticism of compositions. 

1. By pupil acting under general direction of teacher. 
Have first reading for paragraph structure; second read- 
ing for sentence structure covering concord of subject 
and predicate, adjective and noun, pronoun and ante- 
cedent, etc.; third reading for spelling of every word. 

2. By use of the model. Typical composition read 
or written on board, and then each pupil corrects his 
own. 

3. Interchange of compositions. 

4. By the teacher. This is necessary once a month 
as a means of estimating the work of the class, but it 
is not approved for regular weekly criticism. It mort- 
gages teacher's time which should be reserved for rest 
or change of work; it violates the principle of self-activity 
of the pupil; it is practically useless unless the composi- 
tions be returned and the pupils be led to avoid similar 
errors in the next composition. 

349. Suggestions on criticisms. 

1. Teach pupils to consult grammar, dictionary, 
book of synonyms, and any other helpful references. 
This will aid self-criticism and at the same time teach 
pupils how to study. 



152 METHODS IN EDUCATION 

2. Reject all slovenly work and, if due to careless- 
ness, have the composition rewritten. 

3. Do not try to read all compositions. Select a 
representative group and then make these the subject 
of criticism. 

4. Establish a standard of excellence and adhere to 
it. 

5. Treat individual difficulties in brief, personal 
interviews. 

6. Give maximum praise for every indication of 
improvement. 

7. Use constructive criticism. The child must think 
as a child and write as a child. 

8. Assist pupils to clear thinking. The outhne 
aids clearness. 

9. Use a simple code of marking. One is given in 
Maxwell and Johnston's School Composition, page 223. 
Place code on a chart in the front of the room. 

10. Give oral drill on errors found to be general. 

Structural Errors 

350. Too many rules. — We do not expect pupils to 
acquire a finished literary style during eight years in 
the elementary grades, but we do expect to find fewer 
structural errors from year to year. One cause for dis- 
appointment is the number of rules given for guidance. 
Nearly all the points can be grouped under the sentence 
and the paragraph; and the only safe remedy for recur- 
ring errors is to return to a review as suggested in the 
next two paragraphs. 

351. The sentence. — It is a matter of discussion 
whether the sentence or the paragraph should be con- 
sidered the unit in composition. Reserving the decision, 



COMPOSITION 153 

the teacher must teach the individual sentence before 
pupils can become proficient in composition. SpeUing, 
capitahzation, punctuation should be observed in all 
grades; recognition of subject and predicate in primary 
grades; simple, compound, and complex sentences with 
word, phrase, or clause modifiers in grammar grades. 
Neither subsequent construction nor criticism can be 
intelligently done if pupils fail to master a working 
knowledge of the sentence. 

. 352. The paragraph. — If we view composition work 
as a whole, the paragraph is the unit of thought Lower 
primary pupils may be able to think only in sentences, 
but pupils in grades four to six can understand the use 
of the paragraph. The concept of the paragraph is 
most easily secured by the analytic study of a model. 
Such a study will reveal the writer's plan made up of 
beginning, middle, and end; or, as the parts are called 
later, introduction, body, and conclusion. An oral dis- 
cussion of the plan or outline will lead to an inter- 
pretation of this framework of the paragraph; and 
then, following that outline, the pupils may write a 
paragraph; the last process is comparison and criticism. 
This exercise embodies analysis and synthesis. 

Pertinent Questions Answered 

353. Rewriting compositions. — Should pupils he com- 
pelled to rewrite all compositions for the purpose of approx- 
imating perfection f 

No. Such expenditure of time in the correction of 
errors does not seem prudent. Better write another 
composition and thus apply principles of correction. 

354. Occasional rewriting. — Should compositions ever 
be rewritten f 



154 METHODS IN EDUCATION 

Yes, if carelessly done. Have the work done as extra 
work. If pupils write thirty compositions a term, it is 
thought useful to have four or five perfect compositions 
in the set. 

355. Original drafts. — Are original drafts kept for 
reference as an indication of progress f 

Yes. Many teachers prefer to have a separate book 
for composition, so that the pupil may have a guide to 
his own progress. 

356. Ink or pencil. — Are first comes written in ink 
or pencil? 

Pencil in lower grades; ink in upper grades. 

357. Envelopes. — When letters are written, does the 
addressing of the envelope {or rectangle representing same) 
form part of the exercise f 

Yes. 

358. Consulting references. — Do teachers allow pupils 
to consult dictionaries and other such aids during the 
composition lesson? 

Yes. Teach pupils to use all helpful material. 

359. Choice of model. — Should a model be constructed 
by the teacher ? 

No; make a selection from good literature. 

360. Cause of errors. — Are errors due to carelessness 
or ignorance? 

Most of the errors are due to carelessness. The pupils 
rely upon the teachers to find and mark the errors. 

361. Time before criticism. — How long a time usually 
elapses between the writing of a composition and its cor- 
rection by pupils? 

If possible, allow at least two days to elapse. Au- 
thority is against correction during the same period, 
since pupils should not be expected to change their 



COMPOSITION 155 

mental attitude within a period of forty minutes or an 
hour. 

362. Effect of criticism. — Does criticism tend to check 
spontaneity and originality? 

With conscientious pupils, yes; with indifferent pupils, 
no. The tendency toward sympathetic, constructive 
criticism is no likely to produce unsatisfactory results. 

363. No criticism. — Do you ever have compositions on 
which no criticism is made? 

-Yes, to encourage individuality. Let it be known in 
advance that the productions are to be read by the 
writer without oral or written criticism. 

364. Signature of critic. — When pupils correct the 
compositions of others, do you require the critics to sign 
their names? 

Always. This allows the right of appeal to the critic or 
the teacher. It fosters criticism rather than fault-finding. 

365. Colored pencil used. — Should teachers use colored 
pencil or black pen or pencil when they correct compositions 
personally ? 

Colored pencil. Economy of time for teacher and 
pupil in reviewing marking. 

366. Errors indicated. — Do teachers indicate errors, 
or actually correct them? 

Indicate the errors. 

367. Self -correction. — In what grade may self -correc- 
tion he advantageously introduced? 

As soon as pupils are capable of writing a sentence, 
they should begin self-criticism. Their knowledge of 
self-criticism should increase with their general knowl- 
edge. It is a part of self-realization. Hence, self- 
criticism can be justified in all grades above the third. 

368. Time limits. — 7s a time limit assigned ? 



156 METHODS IN EDUCATION 

Yes, in school; on original composition at home, no. 
But it is advisable to habituate pupils to approximate 
time limits at home as well as in school. They must 
meet such requirements in business. 

369. Pupils choose subjects. — Do you ever allow 
pupils to choose their subjects? 

Yes, within specified hmits. Unlimited choice leads 
to vacillation and consequent loss of time. 

370. Reading best work. — Should the best composi- 
tions be read at morning exercises f 

Yes; this establishes an honor standard. 

371. Writing poetry. — Are your pupils encouraged to 
write poetry? 

Yes, occasionally. Every class can produce some 
meritorious poems. 

372. General progress. — Is the habit acquired in 
composition work strong enough to be effective in the written 
exercises in other subjects ? 

Yes, if there is a good spirit among the teachers. 
When a school exacts a certain standard of excellence, 
the pupils respond. 

An Examination Question Answered 

373. The question. — (l) What is the relative value of 
composition in school work? (2) How should outlines be 
used ? (3) Give an effectual method of criticism. (4) Dis- 
cuss the scope and method of correction. 

(1) Composition is one of the most important exer- 
cises in school work. It is a means of expression in all 
the other studies, and it can be made an efficient test 
of general intellectual progress. 

(2) Outlines should be used as guides in the selection 
and arrangement of important points. Pupils should be 



COMPOSITION 157 

taught to make their own outhnes by study and analysis 
of model compositions. Take interesting selections 
from such writers as Hale, Irving, Alcott, Thoreau, or 
any others hked by the pupils; read the selections and 
make a list of the topics. Have children reconstruct 
stories from given outlines and then compare their 
compositions with the model. 

(3) Have compositions read in class and criticised 
favorably by teacher and pupils. Try to arouse the 
interest of the pupils by encouraging them to do their 
best to merit the approbation of their associates. 

(4) Teachers should not pass valuable time in cor- 
recting compositions. Make the pupils critics of their 
own work. In this way the pupils will learn to find their 
own errors, amend them as well as they can, and try to 
avoid similar errors in the future. Following are some 
rules to train pupils to criticise and correct their own 
compositions: " (l) Give the pupil all needful books of 
reference, and teach him how to find what he wants. 
(2) Have the pupil look for only one class of errors at 
one time. He should examine (a) his outhne; (6) his 
sentence structure; (c) his capitahzation, punctuation, 
and spelling. This would necessitate three careful read- 
ings of his composition." See Maxwell and Johnston's 
School Composition. 

Primary Language 

Attention is directed to Plans and Details of Pri- 
mary Language Work, by Catherine L. O'Brien; pub- 
lished by the author of Methods in Education ; 50 
cents postpaid. 

This is a comprehensive treatment of all phases of 
language work in the first four years of the elementary 



158 METHODS IN EDUCATION 

school. The schedule of lessons for daily, weekly, and 
monthly assignment satisfies all the requirements of the 
Elehientary Course of Study in New York City, and 
yet the scheme is flexible enough to suit the needs of 
primary schools in other localities. To give greater 
efficiency in using references. Miss O'Brien has cited 
references by pages for every topic treated in the four 
years of language study. No other one publication 
on elementary language work gives so much specific 
guidance to teachers, principals, and superintendents. 



CHAPTER XI 

GRAMMAR 

374. Value of technical grammar. — A third phase of 
language study in the elementary school is formal gram- 
mar. The works of literary art in the readers, re-enforced 
as they ought to be by supplementary reading at home 
of the whole works from which the selections for the 
school readers are made, will educate the child in the 
use of a higher and better English style. Technical 
grammar never can do this. Only familiarity with fine 
Enghsh works will insure one a good and correct style. 
But grammar is the science of language, and as the first 
of the seven liberal arts it has long held sway in school 
as the disciplinary study par excellence. A survey of 
its educational value, subjective and objective, usually 
produces the conviction that it is to retain the first place 
in the future. Its chief objective advantage is that it 
shows the structure of language, and the logical forms 
of subject, predicate, and modifier, thus revealing the 
essential nature of thought itself, the most important 
of all objects because it is self-object. On the subjective 
or psychological side, grammar demonstrates its title to 
the first place by its use as a discipline in subtle analysis, 
in logical division and classification, in the art of ques- 
tioning, and in the mental accomplishment of making 
exact definitions. Nor is this an empty, formal dis- 
cipline, for its subject-matter, language, is a product 

159 



160 METHODS IN EDUCATION 

of the reason of a people not as individuals but as a 
social whole, and the vocabulary holds in its store of 
words the generahzed experience of that people, includ- 
ing sensuous observation and reflection, feehng and 
emotion, instinct and volition. — Report of Committee of 
Fifteen, page 48. 

375. Scope of this chapter. — In this chapter it is 
not necessary to try to cover every point in grammar. 
Approved text-books suggest suitable methods of pres- 
entation in accordance with the characteristic plan of 
development of such texts. It is necessary, however, 
to present some of the most important and most difficult 
parts; and so we have selected what may serve as types 
in the matter presented and in all related matter. Thus 
the plan of teaching the noun clause is a distinct type 
of mental procedure which may be followed in teaching 
adjective clauses and adverb clauses. 

376. A habit of thinking. — One specific value of 
grammar is the habit of mental activity acquired by an 
orderly way of attacking each sentence. Teach chil- 
dren to read the sentence, to find the principal parts, to 
select and classify the modifiers, and then to dispose 
of the independent elements. Teach the fundamental 
facts; and make all pupils feel that a mastery of the 
simple sentence means a mastery of nearly all gram- 
matical relation. In this way, grammar will not remain 
a synonym for what is difficult or impossible. 

377. Facts before conclusions. — In regard to mental 
processes, teachers are urged to habituate pupils to 
observe the facts first and then draw the conclusions. 
We may illustrate this by taking one sentence, 



GRAMMAR 161 

Pupils work faithfully 

Teacher. What part of speech is work? 

Pupil. Work asserts action; hence, work is a verb. 
Or this answer: Work is a verb because it asserts action. 

These two answers illustrate two mental processes, 
each tending toward a habit. Which process is 
preferred? The former requires attention, thought, 
judgment. It is the empirical, scientific method: 
observation, facts, conclusion. The second process is 
conducive to guessing and inactivity. Answers are 
given quickly, but the responsibility of testing the answer 
is shifted to the teacher. Cross-examination follows 
and frequently induces the pupil to change his opinion. 
Deliberate reasoning in the first instance is a clear gain 
for the pupil even though time is precious. One clear 
concept in the beginning of any process in grammar will 
obviate hours of drill in subsequent work. 

378. The syllogism. — A closer analysis of the mental 
process just mentioned shows that pupils are constantly 
using the syllogism. Thus in the sentence given, what 
part of speech is faithfully? The child observes the 
word and then his thought follows this form: 

Whatever modifies a verb is an adverb. Major 
premise. 

Faithfully modifies the verb work. Minor premise. 
Therefore faithfully is an adverb. Conclusion. 

379. Fundamental facts in grammar. — In treating 
the subject of errors in composition, we reached the 
decision in favor of going back to a simple classification 
under sentences and paragraphs. Some teachers make 
a chart of essentials under words, sentences, and para- 
graphs, and keep that chart in sight for daily use until 



162 METHODS IN EDUCATION 

those essentials become a part of every pupil's mental 
equipment. This is ideal instruction. As technical 
grammar is not usually studied until the fifth or the 
sixth year, any normal child comes to the study of 
grammar with an apperceiving mass which embodies 
two or three years of systematic language work on 
words and sentences and, to a certain extent, on the 
paragraph. The first lessons in technical grammar are, 
therefore, simply an interpretation of EngUsh which the 
child is able to construct or comprehend. The transi- 
tion requires the use of new terms, but the interpretation 
of the sentence is not a new process. Difficulty arises 
because teachers do not hold to the mastery of basal 
facts. Three thoughts deserve consideration: the sen- 
tence, parts of the sentence, parts of speech. Nearly all 
of the relations comprehended in these three are simply 
classified in the following five statements: 

1. The typical English sentence has two principal 
parts, subject and predicate. The subject may be noun 
or pronoun; the predicate must be a verb. 

2. All modifiers of the subject have the nature of 
adjectives. 

3. All modifiers of the predicate have the nature of 
adverbs. 

4. A sentence may have a third principal part, namely, 
a complement. An object complement may be noun or 
pronoun; attribute complement may be noun, pronoun, 
or adjective. All of these parts of speech are known from 
drill on the first three fundamental facts. 

5. Simple sentences may be combined into compound 
or complex sentences by the use of connectives. 

380. Development based upon fundamental facts. — 
It is not supposed that the foregoing classification can 



GRAMMAR 163 

be mastered in one term, but every step in grammatical 
study will be made secure if the child is taught to use 
that criterion during the first term. The syllogism is 
unconsciously used every time a child goes back to test 
himself by one of those five statements. In brief, the 
purpose of such a guide is to teach pupils how to study. 
An elaborate treatise on teaching how to study may 
be more welcome to the disciples of theory, but every 
successful teacher knows that the best results cannot 
b^ secured unless the guiding process is simple enough 
for children to understand and interesting enough to 
follow. This plan has met these two requirements. 
The following procedure suggests the general develop- 
ment under this plan. 

1. Flowers bloom. All is new: sentence, subject, pred- 
icate, noun, verb. 

2. Pretty flowers bloom early. Known, same as 1; 
unknown, adjective and adverb. 

3. The pretty flowers of spring bloom early in our fleld. 
Here we have added another adjective, a pronoun, a 
preposition, and phrases. The adjective and the ad- 
verbial uses of these phrases are known from 2. The 
phrase is simply a new form. 

4. The pretty flowers of spring bloom early and late in 
our fields. Conjunction is new. 

5. Children like daisies. The daisy has petals. Chil- 
dren pluck them. The daisy is the day's eye. The daisy 
is pretty. Who brought the daisies f It was she. 

Here we have the purpose to present third principal 
part of sentence; new, names object and attribute; 
related old, nouns and pronouns and adjectives in third 
part of sentence. 

6. Flowers bloom. Simple. Summer comes. Simple. 



164 METHODS IN EDUCATION 

Flowers bloom and summer comes. Compound. Flowers 
bloom when summer comes. Complex. 

Notes on Plan of Development 

381. Types. — These suggestions embody a basis or 
type of procedure in studying all the related parts of 
a sentence. This matter is merely an outline; more 
material is required for a full presentation. 

382. Independent elements. — The interjection may 
be studied with nominative absolute and other inde- 
pendent elements. 

383. Simple sentence first. — Too much emphasis 
cannot be placed upon a thorough knowledge of the 
simple sentence. Master the declarative sentence first, 
and then the other kinds from form of expression appear 
as easy modifications of the declarative form. All the 
parts of speech, too, may be studied in the simple sen- 
tence. A knowledge of nouns, adjectives, and verbs is 
a direct approach to participles and infinitives; and 
adding the adverb, you have the foundation for all kinds 
of phrases and clauses. See development lessons fol- 
lowing. 

384. Maxims applied. — The process of development 
mentioned employs the maxims known to related un- 
known, simple to complex, from whole to parts. Interest 
is stimulated and apperception is assured. Teachers 
understand, of course, that the study of the simple 
sentence means more than analysis. Synthesis of given 
parts, original construction, reconstruction, filling blanks, 
and the various composition exercises will all be used to 
satisfy the needs of the pupils. 

385. Content of illustrative sentences. — While it is 
advisable to use material that is familiar and interest- 



GRAMMAR 165 

ing, there is no reason for using sentences that do not 
express a valuable thought. The following sentences 
are suitable: 

1. Birds sing. 

2. Respect the flag. 

3. Bees gather honey. 

4. The whale is an animal. 

5. Plants need air and moisture. 

6. Fawns are graceful. 

7. The Mohawk valley is fertile. 

8. The Mayflower sailed from Plymouth. 

9. Icebergs from the Arctic Ocean melt in the Gulf 
Stream. 

10. Magellan's ship sailed around the globe. 

11. The territory claimed by the Dutch was called 
New Netherlands. 

12. Staten Island has an area of nearly sixty square 
miles. 

386. Oral analysis. — This process does not receive 
sufficient attention. When used according to an orderly 
plan, it requires close, accurate thinking; it is a means 
to mental and physical poise; and it has the twofold 
value of developing the power of oral and written expres- 
sion at the same time it is interpreting the oral or written 
expression of others. The diagram becomes more useful 
when it is supplemented by oral analysis. 

387. Diagrams. — A diagram is a graphic representa- 
tion of the grammatical relations in the sentence. Some 
systems are too elaborate for practical use, but a simple 
and reasonable system of diagrams means economy of 
time, interested self-activity of pupils, and co-ordinated 
multiple sense instruction. The rule of limitation of 
use may be put this way: Use diagrams whenever they 



166 METHODS IN EDUCATION 

satisfy the purpose of instruction in grammar. It is 
an abuse of diagrams to make them displace all oral 
analysis and parsing. 

388. Drill. — The schools fail to give adequate drill. 
In the effort to cover the assigned limit of work, teachers 
present new matter day after day and then wonder why 
pupils have not retained the matter which was so care- 
fully presented. The average pupil will not give him- 
self the drill alone; drill is essentially the work of the 
recitation period. It should be simple, specific, frequent; 
and instead of repeating in all the lessons in this chapter, 
we offer the following suggestions for kinds of drill: 

1. Use sentences that clearly illustrate the point of 
the lesson. Unnecessary elements in the sentence are 
likely to draw the attention away from the one point 
under consideration. This is specific, deductive applica- 
tion to complete the inductive process. It is the passing 
from the general notion to the particular notion. 

2. Application in sentences found in the grammar. 
Habituate pupils to use the text-book as authority in 
grammar. 

3. Use sentences in history, geography, reader, etc. 
This is another attempt to show pupils where to find 
suitable material. It tends toward independent study, 
as every pupil has a book; it permits physical adapta- 
bility, according to sight, comfortable position, etc.; it 
is correlation of studies. 

4. Synthesis of sentences from given lists of words, 
phrases, or other elements. This appeals to the con- 
structive instinct of children. It may also be used as a 
stimulus in competitive effort. 

5. Pupils find sentences in books or construct original 
sentences. 



GRAMMAR 167 

6. Memorize mottoes, maxims, or other quotations 
that will serve as typical illustrations. 

7. Apply grammatical knowledge in writing and in 
criticising compositions. 

8. Pupils prepare questions for oral or written review 
or examinations. A good question requires a knowledge 
of subject-matter, and experience proves that the average 
class makes such requisite mastery if the teacher uses 
the questions prepared by the class. 

-9. Correlation as a preliminary drill in primary grades 
before beginning the study of formal grammar. 

389. Parsing literary masterpieces. — The value of 
parsing as an educative process should be approved as 
only one of the useful exercises in grammar. The sen- 
tences used in parsing must satisfy interest and culture. 
The question arises, then, whether we should use literary 
masterpieces for this purpose. Does the dissection by 
analysis and parsing destroy the literary value of the 
selection? We quote from the Report of the Committee 
of Fifteen, page 49. 

*'A training for four or five years in parsing and 
grammatical analysis practiced on literary works of art 
(Milton, Shakspere, Tennyson, Scott) is a training of 
the pupil into habits of indifference toward and neglect 
of the genius displayed in the literary work of art, and 
into habits of impertinent and trifling attention to 
elements employed as material or texture, and a corre- 
sponding neglect of the structural form which alone is 
the work of the artist. A parallel to this would be the 
mason's habit of noticing only the brick and mortar, 
or the stone and cement, in his inspection of the archi- 
tecture, say of Sir Christopher Wren. A child over- 
trained to analyze and classify shades of color — 



168 METHODS IN EDUCATION 

examples of this one finds occasionally in a primary 
school whose specialty is 'objective teaching' — might 
in later life visit an art gallery and make an inventory 
of colors without getting even a glimpse of a painting as 
a work of art. Such overstudy and misuse of grammar 
as one finds in the elementary school, it is feared, exists 
to some extent in secondary schools and even in col- 
leges, in the work of mastering the classic authors." 

390. False syntax. — There is some difference of 
opinion about the advisability of using faulty sentences 
for correction. The objection is supported by the 
argument that the child is more likely to remember the 
incorrect form than the correct form. He will image 
the incorrect form by visualization instead of remember- 
ing the correct form which he reaches through abstract 
reasoning. But this argument is not convincing. The 
writing of the correct form gives the pupils the same 
opportunities for visualization; and, besides, comparison 
and contrast will intensify the impression of the correct 
form. Another consideration in favor of using false 
syntax is the fact that nearly all the leading text-books 
in grammar contain such exercises. See the last section 
in this chapter. 

'' The author is utterly at a loss to conceive on what 
principle the introduction of faulty sentences for cor- 
rection can be objected to. Specimens of bad spelling 
for correction are injurious, because, in English, speUing 
is not reducible to fixed rules, but is for the most part 
a matter of simple recollection, and if the eye gets accus- 
tomed to the look of ill-spelt words, it is often difficult 
to recollect the correct mode of spelling them. Syn- 
tactical errors are of a totally different kind. They 
admit of being corrected on fixed principles; and as the 



GRAMMAR 169 

learner is pretty sure to meet with numerous examples 
of faulty sentences, both in conversation and in reading, 
it seems desirable that he should have some practice 
in the correction of those mistakes .which are of most 
frequent occurrence.. Those who object to exercises of 
this kind should, to be consistent, exclude from books 
on logic all specimens of fallacies given for the purpose 
of correction. Yet those who have studied and taught 
logic are aware that few exercises are more beneficial." 
-V Mason's English Grammar, Ed. 1861, p. 173. 

391. Types of lessons. — The material furnished in 
these lessons is intended to give one sound method of 
presenting each topic, but teachers are not supposed to 
think that there is no other material or no other way 
that can be considered acceptable. No matter what 
the topic for presentation may be, a tactful teacher will 
find other ways of adapting the work to individuals and 
to classes. 

392. Parts of speech. — The one fundamental fact to 
be impressed in teaching the parts of speech is that 
words are classified according to their use in the sen- 
tence. Pupils who work upon this basis find it neces- 
sary to observe the use of a word in every instance rather 
than to rely upon mere memory in giving definitions. 
Another point which needs emphasis is that the words 
must be used in sentences. No word can be classified 
as a part of speech in grammar until that word is given 
a correct use in a sentence. Under this interpretation 
the teaching of nouns, pronouns, or other parts of speech 
from miscellaneous lists of words cannot be justified. 

The old way of teaching the parts of speech required 
pupils to memorize definitions and then apply those 
definitions. It was the deductive method. Modern 



170 METHODS IN EDUCATION 

investigation of the process of learning requires the 
inductive method, as we have already shown. The 
same general plan of teaching all the parts of speech is, 
therefore, a combination of inductive and deductive. 
Let us take a lesson on the noun. 
393. Development lesson on the noun. 

I. Preparation. The preparation in this lesson illus- 
trates an instance where the teacher should not pass 
much time in reviewing the work already covered in 
grammar. It is possible that pupils know the sentence, 
the subject, and the predicate, but it is doubtful if much 
time passed upon reviewing these three terms would 
serve as a useful preparation for a lesson on the defini- 
tion of the noun. Perhaps the best preparation in a 
lesson of this kind is to go directly to the presentation 
after telling the pupils that we are beginning to make 
an effort to tell the names of all the kinds of words used 
in speaking and writing. 

II. Presentation. 

1. Mt. Vernon is in Virginia. 

2. Mt. Vernon was Washington's home. 

3. Mt. Vernon is near the Potomac River. 

4. The house has a large porch. 

5. High columns support the roof. 

6. Martha Washington had a pet cat. 

7. A hole was cut in the door for the cat to enter 
Martha's bedroom. 

8. An old negro watches Washington's tomb. 

9. The tomb is locked. 

10. The keys were thrown into the Potomac River. 

This series of sentences gives enough name words to 
be used in developing the definitions. The series of 
sentences forms one general thought which may be a 



GRAMMAR 171 

source of interest to young children if the teacher will 
fill out some of the details suggested. It is not necessary 
to ask and answer questions here; teachers can use their 
own ways. 

III. Application. Similar sentences may be used in 
applying the definition that a word used as a name is a 
noun. The use of simple sentences will give drill enough 
for one lesson. Succeeding lessons should employ sen- 
tences made from lists of words furnished and also 
OMginal sentences constructed entirely by the pupils. 

394. Development lesson on attribute complement. — 
See section 233. 

395. Predicate adjective and adverb modifiers dis- 
tinguished. 

I. Aim. To determine the correct use of the predi- 
cate adjective and the adverb modifier. 

II. Preparation. Define and illustrate subject, 
predicate, noun, verb, adjective, adverb, and adverb of 
manner. 

III. Presentation.' 

1. That boy appears prompt. 

2. That boy appears promptly. 

3. The sun shines bright in my old Kentucky home. 

4. The sun shines brightly on Kentucky homes. 

5. The horses are running wild on the prairies. 

6. The horses are running wildly from the prairie fire. 

7. The ship returned safe. 

8. The ship returned safely through the rocky 
channel. 

9. The pupils are faithful. 

10. The pupils worked faithfully. 
The presentation is simply an application or drill 
upon the definitions called for in the preparation. The 



172 METHODS IN EDUCATION 

adjectives in sentences 1, 3, 5, 7, and 9 denote a con- 
dition of the subject; the adverbs in sentences 2, 4, 6, 
8, and 10 express manner of performing an act. This 
distinction suggests the rule. Use the predicate adjec- 
tive to denote a condition of the subject; use the adverb 
modifier to express manner. 

IV. Drill. Recall the verbs generally followed by an 
attribute complement, namely, be, become, appear, 
seem, feel, look. 

1. Be kind. 

2. Try to become courteous. 

3. You appear well. 

4. You work well. 

5. This distinction seems easy. 

6. Do you feel good? 

7. Stand and sit erect. 

8. The door stands open. 

9. You will grow taller. 
10. You will grow rapidly. 

For further drill use the device allowing a choice and 
have each choice justified. 

1. awkward, awkwardly. The blind musician felt 
for a place to rest. 

2. good, well. The child worked on his lessons. 

3. glad, gladly. The children appeared when 

they were promoted. 

4. strong, strongly. The cable is made enough 

to support a ton. 

5. kind, kindly. The teacher spoke to the class. 

Correct these errors and give reasons: 

1. How are you? I am nicely. 

2. She looks beautifully. 

3. The team played good. 



GRAMMAR 173 

4. The food tastes very nicely. 

5. Start quick and walk slow. 

396. Personal pronoun and relative pronoun. — This 
exercise is put under one treatment to show the value 
of pronouns in the economy of expression. There is 
material enough here for two lessons. 

I. Aim. To show that personal and relative pro- 
nouns are sources of economy and euphony in expression. 

II. Presentation. 

SECTION I 

1. Lincoln was President. Lincoln delivered the 
Gettysburg Speech. 

2. This is Frank. Frank's declamation won first 
honors. 

3. Mason was an active boy. Mr. Loring liked 
Mason. 

4. See that bicycle. Harry Ransom made that 
bicycle. 

5. The pocketbook was the prize. The pocketbook 
was given to the best speller. 

SECTION II 

1. Lincoln was President. He delivered the Gettys- 
burg Speech. 

2. This is Frank. His declamation won first honors. 

3. Mason was an active boy. Mr. Loring liked him. 

4. See that bicycle. Harry Ransom made it. 

5. The pocketbook was the prize. It was given to 
the best speller. 

SECTION III 

By the use of the relative pronoun each pair of 
sentences can be combined into one sentence. 



174 METHODS IN EDUCATION 

1. Lincoln was the President who delivered the 
Gettysburg Speech. 

2. This is Frank whose declamation won first honors. 

3. Mason was the active boy whom Mr. Loring liked. 

4. See that bicycle which Harry Ransom made. 

5. The pocketbook was the prize that was given to 
the best speller. 

The sentences given in the three sections are closely 
related in wording and meaning so that pupils may 
employ their energies upon the differences in wording. 
Section II illustrates how a personal pronoun may avoid 
the repetition of nouns; the last five sentences illustrate 
how relative pronouns avoid the repetition of nouns 
and also improve the expression by uniting the two parts 
into one good sentence. Test the three sections by the 
sense of hearing and notice the pleasing effect in the last 
five expressions. 

Shall and Will 

397. Meaning and use. — In early English shall was 
the past tense of a verb meaning to owe or to he under 
obligation to do. In its present use with other verbs to 
form the future tenses, shall has lost nearly all of its 
early sense of obhgation excepting in the second and 
third persons. Shall in the first person denotes simply 
future time; in the second and third persons, shall 
denotes promise, command, or threat. 

Will is from another old verb meaning to choose, to 
desire, or to he willing to do. It used to show that the 
subject had the power to determine the action. Will in 
the first person still retains the original meaning, but 
not so in second and third persons. In these two will 
denotes simply future time. 



gr.a:m:mar 175 

Statements and Commands 

398. Rule. — In the first person, shall expresses 
simply future time; in second and third persons, shall 
expresses promise, command, or threat. Will in the first 
person expresses promise, command, or threat ; in second 
and third persons, will expresses simply future time. 

1. I shall go to Europe this summer. 

2. You shall remain here to study. 

.3. He shall study this lesson in grammar. 
4. I will help you. 

0. You will be read}^ for me. 
6. He will work with us. 

399. Rule. — Shall may be used in the second and 
the third persons for prophecies and promises 

1. You shall have your reward. 

2. Thy future shall lead to flowery paths. 

In Questions 

400. Rule. — In the first person, use shall; in second 
and third persons, use whichever auxiliary is expected 
in the answer. 

1. Shall I recite? 

2. Will you read our answers? 

3. Will your father insist on punctuaHty? He will. 

4. Shall your son be punctual? He shall 

Should and Would 

Should is the past tense of shall. Should has the 
same general uses as shall, but should, in all persons, 
retains its original meaning of duty or obligation. 

Would, the past tense of will, is governed by the 
general rules appljdng to ivill. 



176 METHODS IN EDUCATION 

401. Applications. — Give reasons for shall, will, 
should, and would. 

1. Truth, crushed to earth, shall rise again. 

2. We shall study. 

3. We will study. 

4. If I can't pray, I will not make-beheve. — Long- 
fellow. 

5. She could not think, but would not cease to 
speak. — Crabbe. 

6. There is no if in the case. That we shall succeed 
is certain. — Nelson. 

7. The union must and shall be preserved. — Jackson. 

8. Heaven never helps the man who will not act. — 
Sophocles. 

9. I would rather be right than be president. — Clay. 
10. Herodotus wrote as it was natural he should 

write. — Macaulay. 

402. Modes. — The study of all English presupposes 
the desire to interpret good English and to acquire 
facility in writing and speaking good English. Gram- 
marians differ so much about the number of modes and 
about the distinctions between modes that it is not 
necessary to take a young class into these mooted ques- 
tions. Our general plan of development is one of com- 
parison and contrast. So it is in getting the different 
kinds of sentences from form of expression, in distin- 
guishing attribute complement and adverb modifier, in 
developing the function of participles and infinitives. 
So it should be in teaching modes. The declarative 
form of the simple sentence furnishes an illustration of 
the indicative mode. The same thought expressed in 
the interrogative form is another illustration of the 
indicative mode. A thought involving doubt must be 



GRAMMAR 177 

expressed in the subjunctive form; while the imperative 
sentence gives the verb in the imperative mode. The 
following sentences will serve in this development: 

1. The pupils study grammar. 

2. The pupils are studying grammar. 

3. Do primarj^ pupils study grammar? 

4. If you study well, you will understand grammar. 

5. Study diligently one hour each day. 

In helping pupils to discriminate the modes it is useful 
tu impress upon them that the indicative mode expresses 
a fact; the subjunctive mode a doubt; the imperative 
mode a command. The doubt is the only point that is 
really new in this process of discrimination. The pupils 
are familiar with the expressions in the declarative form 
and the imperative form from their study of sentences 
from form of expression. Hence, as an aid in recogniz- 
ing the expression of doubt, direct attention to the use 
of the connectives if, though, except, unless. Note that 
they simply aid in introducing a clause that is likely to 
contain a verb in the subjunctive mode, but the con- 
nectives alone do not make the subjunctive mode. 
Mode is a modification of the verb, not a modification 
of the conjunction. 

403. Drill on modes. 

1. I hate to see things done by halves. If it be right, 
do it boldly; if it be wrong, leave it undone. — Gilpin. 

2. If you know the quotation, you can recite it. 

3. Learn this definition well, and then you can apply 
it easily. 

4. Do you understand the indicative mode? 

5. If you can distinguish the expression of a fact from 
the expression of a supposition, you can distinguish the 
indicative mode from the subjunctive mode. 



178 METHODS IN EDUCATION 

6. The subject of a verb in the imperative mode is 
seldom expressed. 

7. If you are here, you will understand these defini- 
tions. (Fact; we know that you are here.) 

8. If you are present tomorrow, we shall drill upon 
modes in grammar. (Doubt; we are not certain about 
your attendance tomorrow.) 

Participles and Infinitives 
404. The meaning of terms used. — Much confusion 
arises from the different classifications of participles and 
infinitives. This lack of agreement does not produce 
serious consequences in a school where any good text- 
book is followed as an authority, but it is a matter of 
inconvenience to students who have to pass various 
examinations. We meet the terms verbals, adjectival 
verbals, verbal nouns, participles, and infinitives. Any 
word derived from a verb may be called a verbal. Some 
grammarians adopt verbals as the general heading and 
then classify infinitives, gerunds, and participles as the 
three subordinate kinds. So it is done in Longmans' 
Enghsh Grammar, edited by George J. Smith of the 
New York City Board of Examiners. Maxwell treats 
infinitives as a mode of the verb and then puts the 
gerund and the participle under the verbals. Milne 
considers the gerund a form of the infinitive. Reed and 
Kellogg's grammar favors an explicit wording, such as, 
a participle used as an adjective and a participle used 
as a noun. For the purpose of clearness, we summarize : 

Verbals 

1. Participle used as an adjective; verbal adjective; 
or simply the participle. 

2. Participle used as a noun; verbal noun; or gerund. 



GRAMMAR 179 

References 

Longmans' English Grammar, 144. 
Maxwell's Advanced Lessons in English Grammar, 
144, 155. 

Milne's An Enghsh Grammar, 189. 

Reed and Kellogg's Higher Lessons in Enghsh, 65. 

Partici'ples 

405. Lesson on participle used as an adjective. — 

There are three points to be used as a basis in this les- 
son: verb, adjective, noun. In this lesson we present 
the adjective participle. 

I. Aim. To teach the participle combining the 
nature of a verb and the nature of an adjective. 

II. Preparation. Review definitions and illustra- 
tions of verbs and adjectives. 
III. Presentation. 

1. The sun rises. 

2. The sun dispels the mists. 

3. The sun rising dispels the mists. 

4. Evangeline wandered from place to place. 

5. Evangehne, wandering from place to place, sought 
her lover. 

6. Wandering from place to place, she patiently 

waited her lover. 

7. You recited well. 

8. I heard you reciting well. 

9. We, being weary, rested ourselves in the shade. 
Rapid drill upon subject and predicate in each of the 

first three sentences. Emphatic mention of predicate 
verb in each of the three sentences. Then direct atten- 
tion to rising in sentence 3. 



180 METHODS IN EDUCATION 

Teacher. What part of speech is rising? 

Pupil. Rising is a verb. 

Teacher. What is the predicate verb in this sentence? 

Pupil. Dispels is the predicate verb. 

Teacher. Then are there two predicate verbs here? 

If pupils say yes, contrast predicate verb rises in sen- 
tence 1 and rising. If pupils answer no, go at once to 
the question to bring out the adjective use. Is the 
subject sun modified or unmodified? 

Pupil. Sun is modified by rising. 

Teacher. What part of speech, then, is rising? 

Pupil. Rising modifies the noun sun; hence, it is an 
adjective. 

Teacher. Rising is used as two parts of speech, a 
verb and an adjective. We say it participates or par- 
takes of two natures, and so it is a participle. 

Silent reading of sentences 4, 5, 6. Give time for 
thought. The development already done should sug- 
gest to all pupils what they are to find in these three 
sentences. They have before them what, where, and 
how to study. 

Teacher. Who has found another participle? If all 
fail, repeat process of passing from predicate verb in 
4 to adjective participle in 5. 

Teacher. Find the adjective participle in 6. 

Pupil. Wandering is an adjective participle. 

Another Pupil. Wandering is a form of the verb 
modifying the subject pronoun she; hence, wandering is 
an adjective participle. 

If any pupils have failed to discover that the participle 
modifies a pronoun, this last answer should impress that 
fact. It is information from a classmate, not from the 
teacher nor from circuitous development. 



GRAMMAR 181 

Proceed in similar manner with the other sentences. 
Then have definition formed. A form of a verb, not a 
predicate, having the nature of an adjective and a verb, 
is an adjective participle. 

IV. Drill. 

1. The pupils studying grammar are attentive. 

2. Do you know the definition taught yesterday? 

3. See the pupils writing the lesson. 

4. Having finished the lesson, the class marched to 
the gymnasium. 

5. I, knowing your ambition, offered you an oppor- 
tunity for promotion. 

Constructive drill follows this analytic drill. 

406. Uses of participles. 

1. As a noun. 

(a) Subject and attribute. Begging a courtesy is 
selling liberty. 

(6) Object of verb. Pupils enjoy studying history. 

(c) Object of preposition. We receive good by doing 
good. 

(d) Apposition. Invention, applying old ideas to new 
uses, benefits mankind. 

(e) Independent. Generally speaking, interest sus- 
tains attention. 

2. As an adjective. 

(a) Modifying noun. Lessons learned from experience 
are costly. 

(h) Modifying pronoun. Hearing your voice, I re- 
turned. 

407. Distinctions required. — The student must dis- 
tinguish the mere adjective from the participle used as 
an adjective, and the mere noun from the participle used 
as a noun. The mere adjective does not have the nature 



182 METHODS IN EDUCATION 

of adjective and verb. It is simply an adjective and it 
usually precedes the word it modifies. 

1. Concealed resentment is dangerous. 

2. Coming events cast their shadows before. 

3. His soul was the 'pleasing companion of his body. 

4. Beauty is only a doubting good and shining glass. 

5. The growing plant needs light, heat, and moisture. 
The participle used as an adjective has the double 

nature of verb and adjective, usually follows the word it 
modifies, and may have the same complements and 
modifiers that verbs have. 

1. Keep the pupils working. 

2. Start the ball rolling. 

3. The complement is the part completing the sentence. 

4. Participles, or the words partaking of the nature 
of two parts of speech, have many uses. 

5. Here is a paper neatly written, properly punctuated, 
carefully thought out, and placed on the teacher's desk 
at the appointed time. 

The mere noun has a single nature. It is often pre- 
ceded by the and followed by a phrase introduced by of. 

1. The handling of money pleases some people. 

2. Angry feeling is betrayed by the countenance. 

3. The mastery of grammar is a difficult undertaking. 

4. The groaning of the prisoners and the clanking of 
chains were heard. 

5. Our pupils study drawing, sewing, and physical 
training. 

It is argued by some that when drawing, sewing, etc., 
are simply the names of subject-matter in the recitation 
they are nouns. Other authorities hold that as long as 
such words possess anything of the nature of verbs they 
are still to be classed as verbals. Thus Maxwell in his 



GRAMMAR 183 

Advanced Grammar, page 155, classes drawing as a 
gerund. 

John learns drawing. 

Walking is healthy exercise. 

To avoid mooted points on examinations, the student 
is advised to use an object after drawing, singing, etc., 
if he wishes to classify those words under gerunds. 

1. The pupils practice drawing natural objects. 

2. The children enjoy singing songs. 

- 3. Do you enjoy reading English history? 

4. Writing good English is a pleasing exercise. 

5. Spelling ordinary words is not too difficult a task. 
The gerund, or participle used as a noun, has the 

twofold nature of noun and verb, implies or assumes 
action without asserting it, and may take modifiers and 
complements like those of a predicate verb. 

1. We should encourage reading good books. 

2. My going will depend upon your coming. 

3. Persuading by kindness is sometimes the making 
of hard tasks for one's self. 

4. Your studying now will prevent your worrying at 
the close of the term. 

5. In carefully preparing every assigned lesson, one is 
doing one's duty to the class and to the school. 

408. Drill on participle used as adjective; verbal, or 
verbal adjective. 

1. Children come rejoicing. 

2. He fell at his master's feet, weeping. 

3. Wounds made by words are hard to heal. 

4. Your credit being good, I will trust you. 

5. I, being your guardian, expected to have my way. 

6. Rising to reply, Washington stood blushing and 
stammering. 



184 METHODS IN EDUCATION 

7. The treaty having been signed, trade was resumed 
with Spain. 

8. Pronouns denoting the person speaking are of the 
first person. 

9. The region drained by a river system is called the 
river basin. 

10. Columbus, seeking the back door of Asia, found 
himself knocking at the front door of America. — /. R. 
Lowell. 

409. Drill on participles used as nouns; gerunds, or 
verbal nouns. 

1. Let us beware of losing our enthusiasm. 

2. Doing well depends upon doing completely. 

3. What do you think of his writing that letter? 

4. By writing slowly you may learn to write legibly. 

5. Forsaking evil companions is often the first step 
in reform. 

6. All students should form the habit of reading 
poetry. 

7. The object in saihng west was to find a shorter 
route to India. 

8. He that is good at making excuses is seldom good 
for anything else. — Franklin. 

9. Being in a ship is like being in a jail with a chance 
of being drowned. — Johnson. 

10. Talking is like playing a harp; there is as much 
in laying the hands on the strings to stop their vibrations 
as in twanging them to bring out their music. — Holmes. 

410. Drill on participle used as a mere adjective. — 
Here the twofold nature is not considered; the verbal 
forms should be parsed as adjectives. 

1. The breaking waves dashed high. 

2. The creeping night stole up the hills. 



GRAMMAR 185 

3. Education is the moulding force of life. 

4. Here sailing ships delight the wandering eye. 

5. Now toward the early dawning east 

We speed our course away, 
With eager minds and joyful hearts, 
To meet the rising day. 

There, as we turn our wondering eyes. 

We view one constant show, — 
Above, around, the circling skies, 
* The rolling seas below. 

— Cape Cod Song. 
411. Drill on participle used as a mere noun. — Notice 
that these forms are used to name an act rather than to 
express an act. 

1. Slow traveling is tiresome. 

2. The cackling of geese saved Rome. 

3. The visitors joined in the singing. 

4. Giving is more blessed than receiving. 

5. A little learning is a dangerous thing. 

6. The shearing of the sheep in Austraha is done 
by machinery. 

7. The setting of a great hope is like the setting of 
the sun. — Longfellow. 

8. The treatment of drowning is simply to perform 
artificial respiration. — Overton. 

9. Drawing, reading, writing, spelling, physical train- 
ing, and declamation come in the afternoon. 

10. The firing of signal guns was telegraphing by 
sound. It used only the hearing. But there were 
other ways of telegraphing that used the sight. — E. 
Eggleston. 



186 METHODS IN EDUCATION 

Infinitives 

412. Uses of infinitives. 

1. As a noun. 

(a) Subject. To see is to believe. 
(5) Attribute. To see is to believe. 

(c) Object of verb. Pupils like to sing. 

(d) Object of preposition. We are about to sing. 

(e) Appositive. It is easy to find fault. 

(/) Independent. Every object has its face, so to 
speak. 

2. As an adjective. 

(a) Modifying a noun. I have a lesson to teach, 
(h) Modifying a pronoun. Teach them to think. 

3. As an adverb. 

(a) Modifying a verb. They came to study. 
(5) Modifying an adjective. They are eager to study. 
(c) Modifying an adverb. The fruit is ripe enough to 
eat. 

413. Drill on infinitives used as nouns. 

1. Never fear to do right. 

2. Learn to govern yourself. 

3. Your aim should be to govern yourself. 

4. It is not impossible to govern yourself. 

5. To govern yourself is a duty in citizenship. 

6. It is never too late to mend. 

7. It is not all of hfe to live. 

8. To bear our fate is to conquer it. 

9. To dispute about trifles is foolish. 

10. It was proposed to tax the colonies. 

11. To be just is easier than to be generous. 

12. To be plain with you, you have not tried. 

13. It is helpful to study the life of Lincoln. 



GRAMMAR 187 

14. To submit to insult is to give occasion for it. 

15. To cultivate kindness is a valuable part of the 
business of life. — Johnson. 

16. In great crises, it is a woman's special lot to soften 
our misfortune. — Napoleon Bonaparte. 

414. Drill on infinitives used as adjectives. 

1. Have you time to study grammar? 

2. Alger's stories seem to suit boys. 

3. Ask them to sing patriotic songs. 

, 4. Pupils have a desire to appear well. 
5, Columbus did much to calm the sailors' fears. 

415. Drill on infinitives used as adverbs. 

1. There is work enough to do. 

2. Are you anxious to govern yourself? 

3. She is too sensible to be flattered. 

4. You should strive to govern yourself. 

5. You are old enough to govern yourself. 

6. I paused to observe the bird's proceedings. 

7. Call to see me if you happen to pass this way. 

8 Irving's writings were the first to make American 
literature popular in England. 

9. Every morning the Persian wife used to kneel at 
the feet of her husband and ask nine times, " What do 
you wish that I should do?" 

416. The infinitive without to. — The verbs hid, dare, 
feel, hear, let, make, need, see, behold, and a few others, 
are generally followed by the infinitive without to. 

1. The teacher bade the pupils come at one o'clock. 

2. Would you dare swim in the ocean? 

3. Can you feel yourself grow? 

4. Did you hear your mother call you? 

5. Let music swell the breeze. 

6. Make yourself speak distinctly. 



188 METHODS IN EDUCATION 

7. The first division need not do this home work. 

8. Can you see the flag wave? 

9. Behold the soldiers march in solid ranks. 
10. Watch me diagram this sentence. 

A Development Series 

417. Words, phrases, clauses. — This development 
shows how to proceed from the known to the related 
unknown. This lesson aims to secure different forms 
of expression for the same thought; an exercise in ampli- 
fication. 

I. Aim. To increase knowledge of phrases and 
clauses. 

II. Preparation. Review definitions of phrase and 
clause. 

III. Presentation. Recall the simple sentence of tw^o 
words, subject and predicate; then the added adjective 
modifier and the adverb modifier. Have following sen- 
tences on board: 

1. .The athlete is a strong man. 

2. The athlete is a man of great strength. 

3. The athlete is a man who has great strength. 

4. Study here. 

5. Study in this school. 

6. Study while you are in school. 

7. Tell us an historical story „ 

8. Tell us a story about history. 

9. Tell us a story which relates to history. 

10. The guide proceeded cautiously. 

11. The guide proceeded in a cautious manner. 

12. The guide proceeded as a cautious man proceeds. 
Pupils know definitions of parts of sentences, parts of 

speech, phrase, and clause. Now impress word, phrase, 



GRAMMAR 189 

and clause as the three kinds of grammatical elements 
frovi form. 

All read sentence 1. Individuals name parts of sen- 
tence and parts of speech. Teacher underlines strong, 
Visuahze strong. Suggest the purpose of making or 
finding other expressions for the same meaning. The 
direct statement of the purpose of this recitation will be 
enough to encourage a class to select, discuss, and define 
the phrase elements and the clause elements. These 
twelve sentences will furnish the analytic drill. For 
synthetic drill the following italicized words are suitable 
for expansion: 

1. We respect an honorable pupil. 

2. Washington arrived punctually. ^ 

3. An honest effort will be rewarded. 

4. Diligent men are usually happy. 

5. Franklin arose early. 

Note. — The presentation in this lesson is essentially a drill. 
This shows that the five formal steps need not be rigidly followed 
in all lessons. 

418. Drill on adjective clauses. 

1. I that speak unto thee am he. 

2. The evil that men do lives after them. 

3. He is well paid that is well satisfied. 

4. Men must reap the things they sow. — Shelley. 

5. Words are the only things that live forever. 

6. Put your trust in those whom you have tested. 

7. He serves all who dares to be true. — Emerson. 

8. Blessed is he who has found his work. — Carlyle. 

9. He that plants trees loves others besides himself. 
10. Choose carefully those with whom you will 

associate. 



190 METHODS IN EDUCATION 

11. Time, which deadens hatred, secretly strengthens 
love. 

12. Sunday is the golden clasp that binds the volume 
of the week. 

13. That that that that boy used should have been a 
which. 

14. We never tell our secrets to people who pump for 
them. 

15. California is the state whose mines became known 
in 1849. 

16. Self-respect is the noblest garment with which a 
man may clothe himself. 

17. The power which brings a pin to the ground 
holds the earth in its orbit. 

18. He who has resolved to conquer or die is seldom 
conquered. — Corneille. 

19. Memory is the holy paradise out of which we 
cannot be driven away. — Richter. . 

20. It is a behef in the Bible which has served me as 
the guide of my moral and literary life. — Goethe. 

419. Development: Concord of relative pronoun and 
antecedent. 

I. Aim. To show that the relative pronoun need 
not agree in case with the antecedent. 

II. Preparation. Define pronoun, relative pro- 
noun; name the properties of nouns and pronouns. 
III. Presentation. 

1. You are the pupils who make the school. 

2. You are the pupils whose records give this school 
its reputation. 

3. You are the pupils whom the teachers trust. 

4. I dislike an eye that never twinkles. — Longfellow. 

5. Life is a bubble which any breath may dissolve. 
— Greeley. 



GRAMMAR 191 

6. He is a free man whom truth makes free. — 
Dry den. 

7. No man is born into the world whose work is not 
born with him. — Lowell. 

8. Construct a sentence which will have a relative 
pronoun in the nominative case. 

This lesson is an opportunity for real self-activity. 
It is application rather than the presentation of new 
matter. There are four inquiries for each sentence. 

What is the relative pronoun? 

What case is the relative pronoun? 

What is the antecedent? 

What case is the antecedent? 

Thus in the first sentence who is the relative pronoun, 
nominative case; pupils is the antecedent, nominative 
case. Here the pronoun and antecedent do agree 
in case. Take the second sentence. The relative pro- 
noun whose is possessive case; the antecedent pupils is 
nominative case. The pronoun and the antecedent do 
not agree in case. Likewise in 3, 6, 7, and 8. 

IV. Drill. For further effective drill have pupils 
recall, find, or construct sentences to prove that the 
relative pronoun need not always agree in case with the 
antecedent. 

420. Development: The noun clause. 
I. Aim. To outline a plan of teaching the noun 
clause. This plan is a simple way of passing from the 
known uses of nouns by substituting a clause for each 
specific use of the noun. 

II. Preparation. Review uses of nouns as illus- 
trated in the sentences. Say that this lesson in grammar 
will use material taken from a discussion in astronomy. 
Some astronomers say that every star is like the sun in 



192 METHODS IN EDUCATION 

brilliancy, but the stars appear like small lights simply 
because they are so far from us. The statement spoken 
of in these sentences is the statement that stars are suns. 

1. Subject. The statement is beheved. 

2. Object. Some people believe that statement. 

3. Attribute. It is an interesting statement. 

4. Object of preposition. Have you any doubt about 
the statement? 

5. Appositive. This belief or statement is fascinat- 
ing. 

III. Presentation. The preparation has gone di- 
rectly to the points to be emphasized, namely, the 
principal uses of nouns in sentences. The pupils know 
the definitions of phrases and clauses. Now their 
efforts will be directed toward substituting the clause 
for each use of the noun in the sentences given. 

1. That stars are suns is believed. 

2. Some people believe that stars are suns. 

3. The statement is that stars are suns. 

4. Have you any doubt about whether stars are suns? 

5. The statement that stars are suns is fascinating. 

IV. Drill. Two kinds of drill are suggested here, 
namely, interpretation of sentences given, and expan- 
sion. The constructive experience in making sentences 
to illustrate all the uses of noun clause is also advised. 

1. Let us see how the earth revolves. 

2. My desire is that you may become useful men and 
women. 

3. The opinion that children are naturally bad is not 
favored by me. 

4. Have grammarians any proof of what they say? 

5. Nature teaches that there is order in her ways. 

6. That you are ambitious is proved by your record. 



GRAMMAR 193 

7. The question is whether I ought to do it. 

8. Can you understand that a noun clause is used 
hke a noun? 

9. Frankhn learned that self-help is one way to 
success. 

10. Trouble teaches how much there is in manhood. 

— Beecher. 

Further drill by substituting and expansion is valuable 
in teaching the specific uses of noun clauses. Such a 
process in teaching is both natural and logical. It is sug- 
gested that pupils expand the itahcized parts into clauses. 

1. The teacher asked the pupils to study. 

2. We believe in the heroism of Nathan Hale. 

3. Have you read of Arnold's sad death f 

4. The beauty of Mi. Vernon is fascinating. 

5. Grant proved his ability. 
421. Drill on noun clauses. 

1. I saw that you were faithful. 

2. Galileo taught that the earth moves. 

3. We believe that the soul is immortal. 

4. Many men advocate whatever seems popular. 

5. Can he hold the position? is the question. 

6. Where Warren fell is not precisely known. 

7. That he is rich does not mean that he is happy. 

8. The charge is that you have neglected your duty. 

9. Who wrote the Book of Job is not positively 
known. 

10. Much will depend upon how you write your 
answers. 

11. It is not work that kills men; it is worry. — 
Beecher. 

12. The good is always the road to what is true. 

— Hamilton. 



194 METHODS IN EDUCATION 

13. I regret that I have but one Hfe to give to my 
country. — Hale. 

14. " Beautiful creature," said the fox, '* you sing 
like a nightingale." 

15. One would think that the fate of our country 
depends upon who will be our next president. 

16. Have you any explanation of why you say that 
noun clauses are used as nouns? 

17. The world will little note nor long remember what 
we say here, but it can never forget what they did here. 
— Lincoln at Gettysburg. 

18. If ever it is a question whether you or the flag 
must perish, you will instantly choose that it shall not 
be the flag. — W. T. Sherman. 

19. • Have we not learned that not stocks nor bonds 
nor stately houses nor lands nor the product of the mill 
is our country? It is a spiritual thought that is in our 
minds. — Benjamin Harrison. 

20. That the daring barques of the Northmen had 
long before found their way from Greenland to the 
coast of North America is likely, though not certain. 
What is certain is that nothing more came of their first 
visit. — Goldwin Smith. 

422. Connectives : Explanation and drill. — Pupils 
have already had some uses of the conjunction, the rela- 
tive pronoun and possibly the conjunctive adverb. The 
aim of this lesson is to give breadth to their knowledge 
of connectives. This aim may be attained by analysis 
to find illustrative uses and then by synthesis to impress 

those uses. 

I. Conjunctions 

1. Words. Boys and girls study connectives. 

2. Phrases. Pupils study at home and in school. 



GRAMMAR 195 

3. Independent clauses. Some pupils study at home 
and then they recite well in school. 

4. Noun clause. Teachers know that pupils need 
drill on connectives. 

5. Noun clause. Can you tell whether you understand 
this or not. 

6. Adverb clause of time. Careless people speak 
before they think. 

7. Adverb clause of cause. Napoleon was sad because 
he was in exile. 

- 8. Adverb clause of condition. If you understand, 
let us proceed. 

9. Adverb clause of purpose. We study that we may 
prepare for successful living. 

Correlative conjunctions mutually relate to each 
other. They should be placed before similar parts of 
speech or before corresponding groups of words. 

10. Flattery corrupts both the receiver and the giver. 
— Burke. 

11. There is nothing either good or bad, but thinking 
makes it so. — Shakespeare. 

12. Try to observe whether to speak or to be silent. 

13. Man is neither the vile nor the excellent being 
which he sometimes imagines himself to be. — Beacons- 
field. 

Relative pronouns. Used in adjective clauses Who, 
which, what, and that are the common forms. See sec- 
tion 418 for illustrations. The pronoun is often omitted, 
as in the following sentences. 

1. This is the lesson you will learn. 

2. Cicero is the orator you mentioned. 

3. Connectives is the topic the teacher assigned. 



196 METHODS IN EDUCATION 

II. Conjunctive Adverbs 

The name is derived from the double function of 
conjunction and adverb. First illustrations are in 
adverb clauses. 

1. Time. You learn easily when you are interested. 

2. Place. Cattle will graze where the grass is best. 

3. Manner. The Indians live as their forefathers 
lived. 

4. Comparison. New York has a better harbor than 
Baltimore has. 

5. Degree. The greater a man is, the less he is dis- 
posed to show his greatness. — Channing. (Here the 
first the is an adverb modifying greater; the second the 
is a conjunctive adverb modifying the adverb less and 
connecting the two clauses. The principal clause is, 
The greater a man is.) 

Conjunctive adverb in adjective clauses. Why, when, 
and where are the common forms, and they are fre- 
quently associated in this way; reason why, time when, 
place where. 

1. Give a reason why you study grammar. 

2. This is the time when you study grammar. 

3. This is the place where you study grammar. 

4. The child trusts because it finds no reason in itself 
why it should not. — Holland. 

5. Some schools are places where laziness becomes 
habitual. 

6. The place whereto he came was an abandoned mine. 

7. This great world is the mirror wherein we are to 
behold ourselves. — Montaigne. 

8. The play is the thing 
Wherein I'll catch the conscience of the king.. 

— Shakespeare. 



GRAMMAR 197 

9. Not a soldier discharged his farewell shot 
O'er the grave where our hero was buried. 
10. Is patriotism a narrow affection for the spot where 
a man was born? — Fisher Ames. 

III. Relative Pronoun 

See illustrative uses in sections 418 and 419. 

423. Distinctive uses of connectives illustrated. — 
Use in the sentence determines the specific classification 
of connectives. Take as for illustration. 

- 1. Strong men wept as the procession passed. Con- 
junctive adverb of time. 

2. Grammar is as easy as arithmetic is. The first 
as is an adverb of degree modifying the adjective easy; 
the second as is a conjunctive adverb of degree. 

3. Your place has been filled, as you came too late. 
Conjunction. 

4. There are such pupils as one could desire. Rela- 
tive pronoun. 

424. Synthetic drill on connectives. — Construct sen- 
tences to illustrate the following: 

I. Conjunctions 

1. Co-ordinate: and, but, or. 

2. Expressing cause: as, since, because. 

3. Condition: if, unless, except. 

4. Concession: though, although. 

5. Purpose: that, in order that. 

II. Conjunctive Adverbs 

1. Time: when, before, after. 

2. Place: where, whence, whereto. 

3. Degree: as-as, the-the. 



198 METHODS IN EDUCATION 

4. Comparison: than, as. 

5. Why, where, when, introducing adjective clauses. 

III. Relative Pronouns 

1. Who, whose, whom, which, that. 

425. Fill blanks, tell kind of connective, and classify 
dependent clauses: 

1. you have nothing to say, say nothing. 

2. I admire his courage, I consider him cruel. 

3. Do not go the sun has set. 

4. Holmes wrote he amused others. 

5. I am proud I am an American. 

6. any one attempts to haul down the flag, 

shoot him on the spot. — John A. Dix. 

7. We join ourselves to no party does not 

carry the flag and keep step to the music of the Union. 
— Rufus Choate. 

8. There is no language or speech their voices 

are not heard. 

9. He will neither come in go out. 

10. I see no reason you should not succeed. 

11. You cannot succeed you work. 

12. The moon rose the sun had set. 

13. he fails to repay me, I will trust him. 

14. These are the pupils future will determine 

civic questions. 

426. Exercises in false sjmtax. — These sentences 
illustrate many of the common errors in speaking and 
writing. Have pupils read a sentence, tell specifically 
what the incorrect use is, give reason, and then give the 
correct form. ^ 

1. It is me. 

2. I done that. 



GRAMMAR 199 

3. I seen him. 

4. This here one. 

5. Do like I do. 

6. I have got back. 

7. Not as I know of. 

8. I have saw him. 

9. Who do you see? 

10. I had ought to go. 

11. See that there bird. 

12. Can you learn me? 

13. I had rather write. 

14. He had laid down. 

15. Set down and rest. 

16. What are the news? 

17. He was to Henry's. 

18. Don't never do that. 

19. They returned back. 

20. It was her who called. 

21. He must stay to home. 

22. Did you see them men? 

23. Either of the men are rich. 

24. Henry and John is coming. 

25. You hadn't ought to go. 

26. Continue on in this way. 

27. Who does this belong to? 

28. He had near ten dollars. 

29. I have a couple of dollars. 

30. He died with consumption. 

31. I guess I can do this work. 

32. I only want five dollars. 

33. This is the best of the two. 

34. Many words they darken speech. 

35. We had an awful nice time. 



200 METHODS IN EDUCATION 

36. I expected to have seen him. 

37. He had four brother-in-laws. 

38. There is lots of them in school. 

39. The two first men are strongest. 

40. Let you and I study together. 

41. He dropped down into the water. 

42. They differ between one another. 

43. Some one has broke my pencil. 

44. It is funny how long he stays sick. 

45. You are better than me in arithmetic. 

46. I don't like these kind of sentences. 

47. Wanted a room by a man ten feet by fifteen feet. 

48. You are not as careful as you should be. 

49. The general, as well as his soldiers, were taken. 

50. There seems to be no good reasons for tardiness. 

51. At the North and South Poles the latitude is 
ninety degrees. 

52. He spoke his piece clear and distinct. 

53. A lady wants to sell her piano as she is going 
abroad in a strong iron frame. 

54. I went to New York, you know, and when I 
came back, you see, I entered school. 

55. With a few simple words he proved the previous 
speaker to have been mistaken. 

56. He denied but that he was opposed to the law. 

57. San Francisco is the largest city of any city west 
of the Rocky Mountains. 

58. The company which she had taken so much 
trouble to select were not pleased with each other. 

59. The elephant and beaver's instinct approaches 
close to reason. 

60. If any pupil does not understand, let them say 
so now. 



CHAPTER XII 
GEOGRAPHY 

427. The old and the new. — In the widespread 
criticism of old ways of teaching, geography has received 
its full share of censure. Slavish following of the text- 
book, memorizing long lists of names, and the study of 
unrelated facts are among the faults mentioned. The 
new presentation of geography makes man the centre 
of interest by relating all the facts to the welfare of man- 
kind. This is what is meant by saying that " geography 
should be invested with human interest"; and that 
''the aim in teaching geography should be to give the 
pupil knowledge of the earth as it ministers to human 
life." 

Illustrations 

428. The old way. — The old way of studying the 
rivers of the United States required a description of 
each river under the form "rises, flows, and empties." 
Today those three items are subordinate facts in the 
larger effort of finding what each river does to aid agri- 
culture, manufactures, commerce, and the pleasures of 
life. Aside from the use of drainage, the student studies 
the correlated facts of science, literature, history, and 
geography until every important geographical fact be- 
comes a related cause in the past, the present, and the 
future progress of humanity. 

201 



202 METHODS IN EDUCATION 

429. The new way. — " Once there was no geography 
of the Rocky Mountains, for example, except a study 
of their location and elevation and their representation 
on colored maps. Today the student studies its Yellow- 
stone, its Salt Lake, its palisades, parks, and canons, 
but he soon runs aground in the legitimate fields of 
geography, and finds himself encroaching upon the 
territory of geology or botany, zoology, chemistry, 
physics, or mineralogy. Even in an elementary dis- 
cussion of the influences of these mountains upon the 
climate of the continent, many facts must go unexplained 
without the principles of natural philosophy. That 
geography of the Rocky Mountains is incomplete which 
does not include a typical and detailed study of its 
industries, of its mining, smelting, lumbering, herding, 
and its method of agriculture and irrigation. A study 
of the various peoples of the mountains may take the 
direction of sociology, economics, ethnology, and govern- 
ment. The geography of the Rocky Mountains thus 
approached, and only thus, may give a true insight into, 
and an ability to interpret, that part of the world." — 
Heeter, Commercial and Industrial Geography, N. E. A. 
Report, 1907, page 509. 

430. Definitions of geography. — 

1. Description of earth's surface. 

2. Study of concrete environment. — Bagley, Educa- 
tive Process, page 37. 

3. Biological investigations of living matter; political 
and industrial. — Harris. 

4. Science of present appearance of earth^s surface; 
physical. — Parker, Talks, page 27. 

5. Study of earth as home of occupations of man. — 
Dewey, School and Society. 



GEOGRAPHY 203 

6. Study of earth as home of man. — McMurry, 
Special Method in Geography, 

431. Broader educational use. — This modern con- 
ception of the industrial value of geographical knowledge 
is proof enough that the study of geography is more 
than a mere memory process. Present methods of 
teaching employ observation, memory, imagination, 
reason, and judgment in every complete study of a 

topic. 

An Eclectic View 

432. The courses of study. — Several American cities 
have recently adopted courses of study which exemplify 
a kind of common agreement on matter and method. 
No other subject in the elementary schools is so near 
uniformity under our national ideal. One illustration 
of this excellence is seen in New York City. The general 
course of study for New York City was adopted by the 
Board of Education May 27, 1903; revised June 21, 
1905, and June 11, 1907; and the syllabus in geography 
was adopted by the Board of Superintendents in Octo- 
ber, 1905, and revised in July, 1907. This last revision 
embodies the consensus of opinion of the best thinkers 
on this subject, and so some parts of the suggestions on 
geography are taken verbatim, as in sections 433 to 
436 inclusive. 

433. Introductory note. — Geography has been defined 
as '^the study of the earth as the home of man." How 
this phj^sical environment aids or hinders the develop- 
ment of man, and what man has done to modify, adapt, 
and utilize his physical environment, constitute the 
subject-matter of geography. The human feature 
— man's achievements in industry, commerce, and 
political organization — should predominate in the 



204 METHODS IN EDUCATION 

study. As Dr. Harris has stated the proposition, the 
pupil ^'must begin with the natural differences of climate 
and lands and waters and obstacles that separate peoples, 
and study the methods by which man strives to equalize 
or overcome these differences by industry and commerce, 
to unite all places and all people, and make it possible 
for each to share in the production of all." 

The objects of teaching geography may be classified 
as practical, intellectual, and ethical. 

434. Practical purposes. 

1. There are many geographical facts, such, for 
example, as the location and characteristics of important 
cities, mountain systems, and large rivers, which it is 
a disgrace and a misfortune not to know. Every public 
school child must be made to know such matters so 
thoroughly that he will never forget them. 

2. Maps and plans are now constantly used in news- 
papers and in business. The child must, therefore, be 
made to understand their conventional symbols and to 
become expert in referring to them and interpreting 
them. 

3. The child, as a member of a great manufacturing 
and commercial community, should be familiar with the 
resources and productions, raw and manufactured, of 
his own country, and of all countries with which we have 
dealings; he should know the chief markets, home and 
foreign, for our goods; he should learn the quickest, 
safest, and cheapest trade routes; he should be able to 
form conceptions of the kind of goods which home and 
foreign customers require from New York. While it 
cannot be expected that a child's judgment on such mat- 
ters will be highly trained, he should know how and 
where to find such information when he needs it. 



GEOGRAPHY 205 

4. Our current literature, magazines, and news- 
papers assume an intimate knowledge of geography 
on the part of the reader. School training in the sub- 
ject should, therefore, result in the ability to determine 
quickly, by the use of an atlas, gazetteer, or other work 
of reference, the location and characteristics of places, 
the names of which are met with in reading or required 
in business. Special training along this hne is required 
during the last three years of the course, under the head- 
ing, ''Location of places associated with important 
current events." 

435. Intellectual purposes. 

1. Geography may be made to train the observing 
powers. As far as possible everything taught should 
be illustrated from what the child may see in this city. 
This statement holds good not merely of the introductory 
lessons in home geography, but of the lessons throughout 
the course. Representatives of the chief races of men, 
every conceivable product of man's skill and industry, 
every modern means of transportation and communica- 
tion, may be observed in this city, while our parks and 
museums are full of objects of historic and contemporary 
interest. It is suggested that each pupil be furnished 
with a small blank book in which to record out of school 
the results of his observation. 

' 2. It may be made to train the imagination. At 
every step the pupil is called upon to build up conceptions 
of objects unseen and places un visited through images 
derived from things seen, from pictures, and from verbal 
descriptions. 

3. Rightly taught, geography trains the memory. 
The great vice, however, of geography instruction is the 
learning by rote of hsts of names, (rivers, cities, etc.), 



206 METHODS IN EDUCATION 

or the descriptive matter in the text-book. To avoid 
this barren and wasteful process, the facts of geography 
should be linked by natural associations. ''What 
association so strong," asks Professor Laurie, ''as the 
association of all our knowledge of a subject with the 
famiUar objects of our daily hves, out of which we have 
made the teaching of geography spring? What associa- 
tion so strong as the organic connection which this 
mode of teaching estabUshes in the mind? " Names of 
places, whenever possible, should be associated with 
important historical events and with literary allusions. 
4. Geography should also be made, particularly 
during the last three years of the course, to train the 
reasoning powers. When you ask a child to classify 
the natural features of a country, rivers, for example, 
according to some common property, as navigabihty; 
or the products of a country, as necessaries and luxuries; 
and still more when you ask him to generalize after he 
has classified, as, for instance, to determine the status of 
a people after a classification of their products, you are 
training him to reason. 

436. Ethical purposes. — The ethical purposes of 
the teaching of geography are to lead to the moral lesson 
that all men must work and that each man should so 
work that his labor will benefit not only himself but the 
whole community, and that what is true of individuals 
is equally true of nations. "There is probably," says 
Professor Laurie, "no one subject so prolific of matter 
for independent thought and judgment on the affairs 
of life, and the destiny and duty of man. By means of 
it, too, we not merely furnish moral material, so to speak, 
but we extend the sympathies of the pupil, and lay the 
foundation of that sentiment of humanity which is the 



GEOGRAPHY 207 

necessary counterpoise to narrow and parochial preju- 
dices." 

In order that these matters may be more fully under- 
stood, the pupils must also be led to consider the earth 
in relation to the sun, its forms, its motions, and such 
resultant phenomena as the seasons, air and ocean 
currents, and rains. 

437. Col. Parker quoted. — The first steps in geogra- 
phy should give the child the means to imagine that 
which he cannot see. Begin with the forms around 
you; the close and careful study of the chains or ranges 
of hills, valleys, plains, coast-lines, springs, brooks, 
rivers, ponds, lakes, islands, and peninsulas. Study them 
as you do objects in botany or zoology. Take the chil- 
dren out into the fields and valleys; return to the school- 
room; let them describe orally what they have seen; 
then mould and draw it; and, finally, have them describe 
the objects they have seen by writing. Teach them 
distance by actual measurement; boundaries by fences, 
and other limitations; drainage by gutters, and the flow 
of water after a rain. Let them find a spring, and dis- 
cover how the water comes out of the ground. Have 
them bring in different kinds of earth — gravel, sand, 
clay, and loam. I have not time to give you any regular 
order of subjects — if there be one. Begin with one 
object, study it carefully, then take another and combine 
the two, and so on. I wish to call your attention espe- 
cially to the three great means of thought expression: 
first, the concrete expression; second, drawing; third, 
language. The first may be done by mouldings and 
obtained from an iron-foundry. Have pupils tell you 
what they have seen by moulding the form. Second, 
have them draw everything they see in relief and hori- 



208 METHODS IN EDUCATION 

zontally. Third, describe what they have seen orally, 
and then in writing. Use these means continually in 
teaching geography. — Talks on Pedagogics, page 125. 

438. Home geography. — No matter where the school 
may be located, the first lesson in geography should 
be an observation of the facts at hand. Schoolroom, 
school yard, district, town, country, etc., make a series 
in going from the known to the related unknown. But 
what facts should a child know as a basis for geography? 

439. Fundamental facts. — A knowledge of geography 
implies a knowledge of location, direction, form, size, 
and distance. A further analysis might require space, 
time, proportion, and other elements, but our purpose 
is to ascertain useful essentials rather than to try to 
make a complete category. 

440. Early lessons. — Nature study and object les- 
sons are a preliminary preparation for geography. In this 
way pupils acquire the elementary knowledge of soil, 
climate, productions; animal, vegetable and mineral 
life; and the general needs of mank:nd. This concrete 
approach to technical geography invites the use of 
approved methods and devices, and so it is probable 
that the plan is made familiar as a means of getting a 
concept of forms. The woid plan in this use means a 
representation of anything drawn on a plane. Thus 
the point of the pencil is represented by a dot; the 
pointer, by a straight line; the pane of glass, by a rect- 
angle; the face of a cube, by a square; the sphere, by 
a circle. The top of the child's desk furnishes an easy 
plan. Drawn full size, the plan requires actual measure- 
ment; a smaller size calls for the use of proportion and 
scale. Other plans may include the room, one floor of 
the building, the yard, and a part of the district or the 



GEOGRAPHY 209 

city. Right here in this early work distinguish picture 
and plan or map. Show picture and plan side by side. 

441. Points of compass. — The exercises 438 and 
440 may be used in teaching the points of the compass. 
North, east, south, and west can be fixed in mind by 
positions of objects on each desk. Enlarge the applica- 
tion by indicating directions in room, yard, or district. 
Use sunrise and sunset as aids. Locate north star, face 
it, and then apply the old way of stretching arms, right 
toward the east and left toward the west. Mention 
use of shadows and blowing of smoke as means of deter- 
mining directions. Study wall map and apply knowledge. 
Locate a place and have children point to neighboring 
parts and tell directions. For more practical applica- 
tion, have pupils walk toward certain designated places. 
This exercise gives a personal relation to the facts. Its 
use makes pupils reahze that north is not always up 
nor is south always down. 

442. Distance. — Actual measurements of familiar 
things must always be one way of acquiring the concept 
of distance. Time required in travelling, is another 
equivalent of distance, especially with city children. 
The average child will speak of the length of Brookyn 
Bridge as twenty minutes rather than a mile. Distance 
as an element of size in geography is likely to remain 
an imperfect estimate. 

443. Maps. — The study of the schoolroom gives a 
larger conception of shape, size, location, cardinal 
directions, scale, and proportion. The intermediate 
points, northeast, southwest, etc., should be taught. 
The placing of pupils in the principal points in the room 
is a concrete way of sustaining interest. It gives reality 
to the exercise; and right here the pupils can begin to 



210 METHODS IN EDUCATION 

use their constructive imaginations by making little 
journeys in the room. Name directions to and from 
which they travel. The map of the room requires another 
application of measurement according to a scale. Desk, 
library, and other large objects should be located on 
map, but the location of seats should be deferred. Too 
many items lead to confusion. This selection of im- 
portant objects is the first act in the formation of the 
habit of observing the essentials in later map study. 

The next step is simply a larger application of the ideas 
already gained. In cities, it may be a map of one floor 
of the school building; in rural schools, the yard is better 
because it puts pupils into contact with the realities of 
geography. The pupils' homes are still objective points 
of interest, but hills and valleys, woods and growing 
crops are also inviting forms of educative material 
related to the welfare of man. All these are interesting 
aids in fixing locations, applying directions, and training 
the pupils to image a map of all the points observed. 

444. Models. — The exercises already suggested are 
means of training the observation. At the same time 
the memory is developed. When it is not possible to 
observe the actual forms of land and water, models and 
pictures are supplemental aids. Models may be made 
of clay, sand, putty, or paper. Clay and putty are 
serviceable for permanent illustrations. Moist sand 
is desirable because it can be used many times. Paper 
pulp is light and inexpensive, and it is easily colored to 
represent different elevations. The pulp is prepared 
by tearing paper into small pieces, soaking it, kneading 
it, and then draining off the water. It is easily worked 
into shape to represent land forms. Use glue or mucilage 
to fasten it to heavy paper or board. 



GEOGRAPHY 211 

To illustrate rivers, lakes, or other forms of water, 
build the model upon blue or green paper or upon a 
pane of glass. Then mould the land forms but leave 
paper or glass exposed to illustrate water, 

445. Constructive imagination. — The use of observa- 
tion as a process in elementary work in geography has 
already been shown. Likewise for the first uses of the 
memory in retaining geographical information. As 
sogn as pupils are required to think of forms or conditions 
which they have not observed, the constructive imagi- 
nation is brought into use. A familiar pond may be 
enlarged by the constructive imagination to make a 
lake; the neighboring hill can be increased in size till it 
becomes a mountain; the valley stretches to limits 
beyond the power of human vision, and it becomes a 
plain. All the facts observed in home geography are 
applied to locations in other parts of the earth; the 
streets, the houses, and the public buildings in the native 
village have to be transplanted and modified to make 
the image of a foreign city. Thus it is that in nearly 
every mental act in the broader study of geography the 
constructive imagination presents to the mind the images 
of things which can be thought although they are not 
actually observed. This power of the mind is also 
employed in constructing models, making maps, in 
getting the thought from oral or written descriptions, 
and in making commercial trips to the principal ports 
of the world. 

446. Analytic and synthetic methods. — The analytic 
method of teaching geography begins with the globe as 
a whole. It divides the surface of the earth into land 
and water and then subdivides the surface into islands, 
peninsulas, continents, rivers, lakes, oceans, etc. The 



212 METHODS IN EDUCATION 

advantages claimed for the analytic method are the 
following : 

1. Whole to parts. 

2. Early familiarity with the globe. 

3. Better view of relative position, size, form, divisions 
of land and water. 

4. The globe enables the teacher to explain causes 
of day and night, change of seasons, etc. 

447. Synthetic method. — The synthetic method of 
teaching geography begins with the geography of the 
home and the schoolroom and then proceeds to the 
school yard, the neighborhood, and the larger pohtical 
divisions. It begins with the island, peninsula, valley, 
hill, river, or lake, which the child can see, and then pro- 
ceeds by use of the imagination to the other forms which 
the child cannot see. The advantages claimed for the 
synthetic method are the following: 

1. Interest in familiar objects. 

2. Known to related unknown. 

3. From the near to the remote. 

4. Concrete to abstract. 

5. An inductive method. 

6. It gives the pupil a fundamental geographical 
knowledge and enables him to pursue the study alone. 
In other words, it is a direct way to self-activity. 

448. Both methods combined. — Both analytic and 
synthetic methods are used. The latter is used in 
beginning geography in 4A, the pupils making a map 
of the schoolroom and one floor of the school building as 
an introduction to the study of the map of the City of 
New York. Home geography covers location, nationali- 
ties and local history in such a way that the pupils 
become familiar with the industrial, social and civic rela- 



GEOGRAPHY 213 

tions. The analytic treatment of the earth and its sub- 
divisions is also given in 4A, using the globe. Thus 
the advantages claimed for both methods are utihzed. 

449. Excursions. — Excursions to fields, parks, and 
museums, to docks and water fronts, to centres of local 
industry, manufacturing estabhshments, and sources 
of supply, and to historical buildings, monuments, and 
tablets are recommended. Constant appeal should be 
m^de to the individual observation and judgment of 
pupils. — Introductory Note in Geography, New York 
City Course of Study. 

The mode of learning facts by means of excursions is 
a concrete approach to vivid ideas. A preliminary dis- 
cussion in the classroom prepares the mind for immedi- 
ate and active receptivity in the fields. The facts of 
local environment are learned so that pupils may begin 
early to adjust themselves to their environment. 

A second value of such facts is the acquisition of types 
of knowledge. These types are employed by comparison 
and contrast in studying similar facts or conditions in 
other parts of the world. Remember that the excursion 
itself is not the type of knowledge; the type is what is 
learned. Thus the study of a gas plant is a type for 
the study of other gas plants; one bicycle factory 
furnishes data for a type of knowledge in that hne. 

A third value of information acquired on excursions 
is economy in the act of learning. The lesson is concrete; 
the conditions are interesting; the class is under social 
stimulus; exercise, circulation, and respiration favor 
good physical support for mental activity. 

Fourth, the facts acquired do not admit adequate 
presentation within the scope of elementary text-books. 
Take, for instaince, a canal. The topic is the construe- 



214 METHODS IN EDUCATION 

tion and operation of a lock. A quarter of an hour in 
observing the passage of a boat from a lower level to a 
higher level will give an intensity of impression that is 
not within the possibility of schoolroom teaching. 

Fifth, correlation of industries. Actual contact with 
the various unified forms of industry will tend to put 
the children into sympathy with the conditions requiring 
co-operative adaptation in later life. 

450. McMurry on excursions. — A detailed treatment 
of excursions and types in teaching third and fourth 
grade geography is given in Special Method in Geography, 
by Charles A. McMurry. (The MacMillan Company.) 

Committee of Ten Quoted 

451. Order of treatment. — The Report of the Com- 
mittee of Ten, page 211, suggests an order of treatment 
based on mental processes. (Quoted in sections 451 to 
455 inclusive.) "Reduced to a sentence the scheme is: 
first, see; next, reproduce; then study the productions 
of others, and, meanwhile, ponder and reason on all. 

452. Representative geography. — Immediately after 
the making of observations should come their reproduc- 
tion in the form of descriptions, sketches, maps, models, 
etc. The instruction of the teacher falls short of its 
highest efficiency if the early work is merely observa- 
tional and receptive. The great end of education is to 
create productive ability. One important form of this 
is representative production. Besides having value in 
itself, the description of features that have been seen 
and their representation by sketches, maps, or models 
reacts upon the observational work and induces a clear- 
ness, sharpness, and definiteness that it would not other- 
wise be Hkely to take. Not only this, but it leads the 



GEOGRAPHY 215 

scholars to realize what maps, descriptions, etc., really 
mean. 

453. Derivative or descriptive geography. — When 
pupils have gained true and vivid basal ideas by observa- 
tion and have, by reproducing these, acquired a realistic 
sense of the meaning of maps and an ability to read them, 
in the full and proper sense of the term, they are prepared 
to pass on to a formal study of descriptive geography. 
In . this, the observational and representative work of 
others than themselves is made the basis of study. The 
pupils are not now studying the earth's surface but ' sl 
description of the earth's surface.' 

454. Rational geography. — It has already been urged 
that the pupils should be induced to observe changes 
and processes as well as the simple passive facts of 
geography, and that there should thereby be laid the 
foundation for an understanding of the origin, the devel- 
opment, and the future history of geographic features. 
This is the introduction of rational geography, as dis- 
tinguished from the mere noting and memorizing of 
facts. This phase of the subject, which leads the pupils 
into the reason of things, should be assiduously culti- 
vated, for it is the soul of the science. It should, how- 
ever, be carefully adapted to the capabilities of the pupils, 
particularly in the earlier stages of the study. They 
should not be forced beyond their capacity to compre- 
hend the nature of the agencies that have rendered 
geography what it is. On the other hand, there is an 
equal danger of underestimating the capacities of pupils 
to see into the reasons for natural operations. 

It is not recommended that rational geography be 
disassociated from observational and descriptive geo- 
graphy, but rather, on the contrary, that it be intimately 



216 METHODS IN EDUCATION 

connected with these and that it be introduced so as to 
give them Ufe and significance. 

455. Observational geography. — In the judgment 
of the Conference, observation should go before all other 
forms of geographical study and prepare the way for 
them; its object being (1) to develop the power and habit 
of geographic observation, (2) to give the pupils true 
and vivid basal ideas, and (3) to arouse a spirit of in- 
quiry and a thirst for geographical knowledge. This 
work of observation should begin with those features 
that lie immediately about the pupils and so fall easily 
within the reach of their direct study and ready compre- 
hension. In rural districts, the natural features of the 
surface will obviously form a large part of the study, 
while in cities, the artificial features must largely take 
the place of these. In the one instance, natural geogra- 
phy, as seen in the forms of the land, the hills, valleys, 
plains, meadows, divides, streams, lakes, etc., will pre- 
dominate, while in the other artificial, or humanistic 
geography will receive leading attention, as streets, 
railways, wharves, harbors, parks, plots, wards, etc.; 
but something of both these groups of subjects may be 
found and utilized in both localities. Neither should 
be neglected, for the pupils need not only to acquire 
clear ideas of the things by which they are chiefly sur- 
rounded, but type ideas of the things which characterize 
other localities and of which they need to form correct 
ideas without being able to see them. Observation, 
however, should not be confined simply to the passive 
fixed features by which pupils are surrounded. They 
should observe the agencies that produce surface changes, 
such as winds, rains, floods, thawing, freezing, cultiva- 
tion, etc. The temporary streams that follow heavy 



GEOGRAPHY 217 

rains represent on a small scale many of the natural 
processes by which surface features are produced. From 
these immediate agencies, the observations should extend 
to the phenomena of the weather and the cHmate, such 
as temperature, winds, clouds, seasons, etc. ... As a 
step toward the study of the distribution of plants 
and animals, and an insight into their dependence upon 
temperature, soil, food, etc., the pupils should be en- 
couraged to observe the differences of plants on uplands, 
lowlands, marshes, etc., and upon sandy, clayey, gravelly, 
or stony ground, and to note the habitual dispersal of 
animals and insects in the neighborhood, and also their 
relations to each other, as in forming or frequenting 
forests, prairies, meadows, etc. As a step toward the 
study of the human elements in geography, observations 
should be made upon the population and its distribution, 
upon home occupations and productions, upon local 
political boundaries, as wards, school districts, city or 
town limits, etc., and upon the location of cities, villages, 
railways, canals, etc. 

456. Concentric circles. — The arrangement of subject- 
matter in any course of study may be made so that the 
elementary facts of a subject are treated as fast as pupils 
are able to master those facts. Then in a later grade the 
more difficult facts are presented after a review of the 
elementary facts already mastered. This process of 
enlarging the scope of knowledge as pupils pass from 
grade to grade has been termed the arrangement in 
concentric circles. Many of the new text-books in the 
various subjects are made according to this plan. The 
old method attempted to master all essential knowledge 
of any part of a subject before passing to another chapter 
which dealt with another phase of the same subject, It is 



218 ♦ METHODS IN EDUCATION 

claimed that the plan of concentric circles is in harmony 
with the interest and the ability of pupils. 

This arrangement in concentric circles, or cycles, is 
known as the spiral method in geography. This plan 
of arrangement is used in nearly all the modern courses 
of study, although there are some adverse criticisms of it. 
In teaching the circle of simpler facts, some teachers 
fail to give enough information, while others pass beyond 
the elementary circle into the fields of information which 
are supposed to be reserved for another grade. These 
two conditions are likely to make children show a lack 
of interest as soon as another teacher begins to review 
or enlarge the circle of information already covered. 

457. Illustration of concentric arrangement. — The 
following outline for five grades illustrates the cycles 
in geography. 

4A. Home geography, local history, the earth. Form 
and surface; the continents; the oceans; great islands 
and groups of islands; great seas, gulfs, and bays. 

4B. The earth: motions, zones. Eastern and western 
hemispheres, world stories, duties of citizens and pubHc 
officials. 

5A. The earth: seasons, latitude, longitude. General 
study of North America and United States. 

5B. United States: representative states in each 
group. New York and the City of New York. 

6A. South America, Canada, Mexico, Central America, 
and West Indies. Location of places associated with 
current events. 

6B. Europe. Location of places associated with cur- 
rent events. 

, 7A. Review of United States and its dependencies. 
Places and current events. 



GEOGRAPHY 219 

7B. Asia, Africa, Australia, and Island Groups. 
Places and current events. 

8A. Mathematical and physical geography. Places 
and current events. 

8B. Review of political and commercial geography. 
Places and current events. 

458. Causal relations. — In the study of geography 
it is possible to memorize all the important facts about 
topography, climate, and human progress, but that 
knowledge would not be considered satisfactory in con- 
tent or method. Every part should be associated with 
cause and effect. Topography modifies climate and 
both topography and climate affect man. Man, in 
turn, converts many of the physical conditions to his 
own advantage. The tracing out of all these mutual 
conditions as causes and effects employs the reasoning 
powers in getting what is known as causal relations. 

459. Causal series. — Recall the criticism of the old 
ways of teaching geography by making it a memory 
process. The explanation of causal relations already 
given is another way of showing that the modern teaching 
of geography appeals to the other powers of the mind. 
The processes required for reason and judgment are 
employed in all phases of the work from 4A through 8B. 
The arrangement of topics in such a way that the causal 
relations appear as a series gives rise to the term casual 
series. The following topics constitute a causal series: 
(1) Location, (2) resources, (3) industries and occupa- 
tions, (4) products, (5) commerce, (6) chief cities, (7) 
social development. See latest outline suggested in 
Plan of Study for 1907, section 466. 

460. Man and nature. — Thus the interpretation of 
causal relations in geography involves the reciprocal 



220 METHODS IN EDUCATION 

relations of man and nature. We quote from an article on 
Commercial and Industrial Geography by Superintendent 
Heeter of St. Paul, N. E. A. Report, 1907, page 508. 

" While cHmate and topography have operated singly 
and together in the distribution of life and both have 
played an important part, not only in the making of 
history, but in determining the customs and achieve- 
ments of every people, yet man has not been a slave to 
geographical conditions. He has gone forth to modify, 
to rise above environment, to multiply, and to subdue 
the earth, and there is a human, as well as a natural, 
interest in all this new study. 

'Tis true, man has populated the earth, the North- 
land and the Southland, from Scandinavia to Siberia, 
from Abyssinia to the islands of the sea, but wherever 
he has gone, he has clad himself to meet the conditions 
of climate; he has built to withstand the tests of season; 
he has labored for wholesome food; and has forced the 
earth to yield up more than her native stores. The 
very form and character of his effort, as revealed by the 
apparatus in organization of industry, show not only 
the process of adjustment to native environment, but 
a determination and a success in rising above all natural 
limitations. Thus the Esquimau labors and invents, 
but not the same as the nomad of the desert, the planter 
of the flood-plain, the ranchman of the foot-hills, or the 
lumberman of the camps. The great double, question, 
then, confronting the student of geography today is, 
first, what physical and climatic conditions have directly 
influenced the different peoples of the earth, their modes 
of life, and their activities? Second, what have these 
people in turn done reacting against their geographical 
environment? 



GEOGRAPHY 221 

Under the stimulus of man's inventive genius, along 
with the evolution of modern science and inventions, 
intercommunication has been made perfect, barriers 
have been broken down, regions once isolated have been 
connected, continents have been linked, the whole earth 
has become one vast neighborhood, and every man a 
neighbor. Here we see the interdependence of men, 
the East upon the West, the West upon the East, the 
North upon the South, and Europe upon America. 
Adverse conditions in one section affect all other sections. 
Civilized man everywhere is dependent upon all regions 
of the earth to contribute to his food, shelter, clothing, 
and culture; and a large part of civilized effort has been 
directed toward perfecting modes of travel, commerce, 
and intercommunication, until today streams of trade 
have opened into world-wide currents." 

461. Types in geography. — A type in any study is a 
form of knowledge fixed in the mind. Such a form of 
knowledge becomes an apperceiving group for all other 
related knowledge. Thus in the study of geography it 
is possible to have the child master a characteristic 
mining section, or an agricultural section, or a manu- 
facturing section. Then when he comes to study other 
portions of the globe situated within the same general 
boundaries, his first inference will be that the conditions 
in those respective mining, agricultural, and manufac- 
turing sections are similar to the ones already studied. 
The analogy must be tested by finding a few conditions 
that mark a difference between the two sections. The 
advantages claimed for types as given by McMurry are 
the following: 

1. Types are keys to larger areas of geographical 
knowledge. 



222 METHODS IN EDUCATION 

2. Realities are studies. 

3. Thoroughly interesting and instructive. 

4. The study of causes and causal relations. 

5. Basis of a series of comparisons. 

6. From home outwards. 

7. Direct path to whole groups and sequences. 

Illustration of Type 

462. Home city a type. — In 4 A grade the pupils 
make a thorough study of New York City. Note how 
this kind of treatment could be applied to Boston, 
Chicago, San Francisco, or any other city. 

Home Geography. — A plan of the schoolroom as 
an introduction of the study of maps; sketch plan of 
the school block, showing the position of the school 
building and the location of the classroom; the directions, 
north, south, east, and west indicated; plans drawn 
without reference to scale. Topography of the City of 
New York and vicinity; location of city with reference 
to the states of New York and New Jersey; division of 
city into boroughs and names of boroughs; direction of 
each borough from home borough; boundaries of the 
home borough and of Manhattan; land and water forms 
of the neighborhood; the harbor and water fronts. 
Location of main avenues and streets of home borough; 
names and locations of local bridges, tunnels, parks, and 
other important points of interest, with their attractions 
and the means of reaching them . 

Population. — Brief reference to nationalities com- 
posing it; occupations of the people illustrated by 
reference to neighboring farms, factories, shops, and to 
street and river traffic; transportation of people from 
the home borough to the business sections. 



GEOGRAPHY 223 

Local history. — Stories connected with the history 
of New York told or read by the teacher or by the class; 
stories illustrated by reference to places and monuments 
of historic interest; biographical stories illustrating 
some of the great historic periods, as the settlement of 
Manhattan and neighboring territory; Dutch occupa- 
tion; the coming of the Enghsh; struggles with the 
French and with the Indians; New York during the 
Revolution. Department of the city as a manufactur- 
ing and commercial centre, e.g., Fulton's steamboat; 
the opening of the Erie Canal; the introduction of the 
telegraph; the laying of the Atlantic cable; the Brooklyn 
Bridge; consolidation; the Greater New York; the open- 
ing of the subway. 

Stories of distinguished citizens of the City of New 
York, such as Peter Stuyvesant, DeWitt Clinton, and 
Peter Cooper. 

Good citizenship. — Fire Department. Fire alarms; 
engine houses; duties of firemen; instances of heroism. 

Duty of Citizens. Care in the use of matches, kero- 
sene, gas, benzine, and other explosives or combustibles; 
care in regard to fireworks, bonfires, and rubbish; duty 
of keeping fire-escapes clear of encumbrances; fire- 
drills; means of egress from buildings; behavior at 
panics. 

PoHce Department. Enforcement of law; mainte- 
nance of order; control of crowds; protection of life and 
property; detection and prevention of crime; arrest 
of criminals; traffic regulation; instances of heroism. 

Duty of Citizens. Respect for pohce authority; 
appeal in case of danger; rendering assistance in main- 
taining order; conduct in the streets; ball-playing and 
stone-throwing — why forbidden ; protection of city 



224 METHODS IN EDUCATION 

property. — From Syllabus, Revised Course of Study, 
1905. 

463. Comparison. — The study of geography by 
means of causal series, topics, etc., requires the constant 
use of comparison and contrast. But even aside from 
these specific methods involving the causes, many modern 
geographies present comparative tables for visualization. 
Some use dark lines of varying lengths to indicate the 
quantity of products. Others approach nearer the 
objective reality by presenting bags of different sizes 
to indicate the quantity of grains produced; barrels 
are used for wines, liquors, and other liquids. These 
tables whatever they may be, are simply another way of 
impressing geographical facts through multiple sense 
instruction. The memory alone is not required to 
carry the lessons of comparison. 

Illustration of Comparison 
North America 

1. North America is an irregular triangle. 

2. On its west coast there is a high range of volcanic 
mountains. 

3. Parallel with the east coast runs a lower range. 

4. The middle of the continent is occupied by a vast 
plain, from the Arctic Ocean to the Gulf of Mexico. 

5. The St. Lawrence flows from west to east; the 
Mississippi from north to south. 

South America 

1. South America is a regular triangle. 

2. On its west coast there is a high range which 
contains many volcanoes. 

3. Parallel with the east coast runs a secondary range. 



GEOGRAPHY 225 

4. The middle of the continent is occupied by a vast 
plain from the Caribbean Sea to the La Plata. 

5. The Amazon flows from west to east; the La Plata 
from north to south. 

This arrangement of facts is taken from DeGraff's 
School Room Guide, page 286. 

How to Study 

- 464. A plan suggested. — It is a rehef to a faithful 
teacher to get a plan that can be used without general 
revision. This does not mean that rigidity is welcomed 
as a characteristic in place of flexibility, but it does mean 
that the practical educator welcomes any suggestion 
based upon successful classroom experience. The fol- 
lowing six sections embody the recommendations by 
the Board of Superintendents in New York City in 1907, 
but the suggestions apply in New Orleans and Seattle 
as well as in New York. 

465. Continents as wholes. — In studying the conti- 
nents as wholes, attention should be directed to their 
comparative sizes (North America being taken as the 
unit), relative positions, their general contour, their 
great mountain systems, their great rivers, their large 
seas, gulfs, and bays, and their important neighboring 
islands. Then should follow the main political divisions 
and the positions of important cities. 

466. Plan for studying a country. — In studying a 
country the following series of topics, as far as they may 
be applicable to the country under consideration and in 
the grade in which the lesson may be given, is suggested: 

1. Location as determined by latitude and longitude 

and with relation to surrounding countries and waters. 

Pupils should never be told the latitude and the longi- 



226 METHODS IN EDUCATION 

tude nor required to memorize them, but should be 
trained to determine them by the inspection of a map. 

2. Comparative size and shape. 

The area of the State of New York (about 50,000 
square miles) may be taken as the unit with which the 
areas of all countries shall be compared. The compara- 
tive size should never be told, but should be made a 
matter of calculation on the part of the pupil. 

3. Mountain systems and important ranges; slopes 
and plains. 

4. River systems and important rivers. 

5. Important cities, their location, and their com- 
parative population. 

The population of the City of New York, four miUions 
in round numbers, may be taken as the unit of com- 
parison. When learning about a city, the reason for 
which it is celebrated should be brought out. 

6. Chmate, industries, products, and areas of pro- 
duction. 

7. Form of government and general condition of 
the people as to education and ways of living. 

Under the head of ''Ways of Living" should be 
included housing, food, clothing, occupations, and use 
of animals. 

8. Exports and imports, trade, particularly with the 
United States. 

467. The recitation. — Most of the work in geography 
should be done in the classroom. Very little, if any, 
study at home is necessary. The lesson should generally 
begin with a study of a globe or a map. This should 
be followed or accompanied by the reading pertinent 
selections from the text-book or supplementary reader. 
The selections should be read aloud in class, and pupils 



GEOGRAPHY 227 

should be expected to answer questions after a single 
reading. Then some time should be spent in copying 
the map roughly from the book or from the wall, indi- 
cating such phases of the subject as have been studied. 
The next lesson should consist largely in questioning 
the pupils with the map before them and in requiring 
them to make rapid sketches of maps from memory. 
This exercise is the best method of fixing geographical 
knowledge and of showing the pupil how accurate or 
inaccurate his knowledge is. It is, moreover, the easiest 
way to teach much of this subject, as well as the easiest 
way to test the definiteness with which the subject has 
been learned. Care should be taken to see that these 
maps are only sketches and that time is not wasted on 
the unnecessary elaboration of details. Neither tracing 
nor construction lines should be used. Sand or clay 
modelling may be used in the early grades to give a 
conception of the surface of a continent or a country. 
468. Use of pictures. — A valuable aid to instruction 
in geography is a picture. The only true conceptions 
of certain elements of geographical knowledge are 
obtained by travel and observation. But travel and ob- 
servation for children are restricted within very narrow 
limits, and the best substitute is the picture. One 
picture is often worth volumes of verbal description, 
and at the present time there is scarcely any place or 
any feature of life or human activity of which a picture 
is not easily obtainable. Pictures are useful, however, 
only when children are trained not only to see and name 
the objects they contain, but to draw conclusions from 
them regarding the character of vegetation, the habitat 
and habits of animals, the ways of living and occupations 
of men, and other topics involved in the teaching of 
geography. 



228 METHODS IN EDUCATION 

469. Outlines by pupils. — In the higher grades, 
pupils should be exercised in making synoptic outlines 
of topics treated in the text-book. 

470. Aids. — Globe; outline, commercial, United 
States geographical survey, topographic and census 
maps; weather charts, pictures, photographs, lantern 
slides, and other illustrative material; collections of 
minerals, rock, soils, seeds, raw and manufactured 
material; text-books, books of reference on geography, 
history, biography, travel, natural history; magazine 
articles, newspaper clippings, almanacs of the New York 
dailies, railroad and steamboat guides, and official 
reports. 

471. Dr. Maxwell on geography. — In September, 
1907, Dr. Maxwell dehvered an address before the 
principals of New York City. Sections 472 and 473 
give the substance of his remarks on the revised syllabus 
in geography. See School Work, November, 1907, for 
an excellent abstracts of the whole address. 

472. Suggestions to principals. 

1. That you read and discuss with your teachers the 
Introductory Note, which explains the organizing princi- 
ple of the course and make suggestions as to method. 

2. That you should take up lessons with your teachers 
as they will be expected to take them up with their 
pupils. These things require special attention to the 
following details: 

(a) How to use a globe. See section 484. 
(6) How to use a map. See section 502. 

(c) How to study the text of the geography. See 
section 504. 

(d) How to study a picture. Following plan suggested : 
Select a picture, see the items it contains, draw con- 



GEOGRAPHY 229 

elusions as to character of vegetation, occupations of 
men, ways of living, etc. 

473. Results that are essential. 

1. In learning about a place, a pupil should be able 
instantly to point to it on (a) a map with names, (b) 
map without names, (c) place it on a map rapidly 
sketched by children. 

2. Tell why it is distinguished. 

3. To make rapid computations as to relative size; 
continents with North America; countries with New 
York State; cities with New York. 

4. To tell the latitude and longitude of a place from 
inspection of a map; and to locate a place, the latitude 
and longitude being given. 

5. To make a synoptic outline of a given portion of 
the text. To meet criticism, I would suggest that both 
teachers and children should be required when mention- 
ing any city in the United States to mention along with 
it the state in which it is located. 

Suggestions for Devices 

Some of these have already been mentioned, but we 
present them all under this heading so that the teacher 
may view the topics as a whole. 

474. Concrete aids. — Moulding-board, globe, maps. 
See section 470. 

475. Outline maps. — The time required for elaborate 
work in making the outlines of various states or countries 
is no longer considered useful in the study of geography. 
Outline maps may be secured from publishers and then 
the filling in becomes a valuable act of learning. Only 
the most important points deserve location on the maps. 



230 METHODS IN EDUCATION 

The use of such map-making is simply one means of 
impressing through visuahzation and motor activity. 

476. Product maps. — Product maps to illustrate 
resources. Concrete interest is attached to this kind of 
work as long as pupils are encouraged to place actual 
resources such as grains, minerals, kinds of trees, etc., 
on the map. 

477. Scrap-book. — Have a bulletin or scrap-book for 
interesting articles brought by the children. The latter 
is recommended for permanent use. The teacher may 
find it necessary to reject some of the material selected 
by the children, but after a little experience the children 
will themselves be able to select what is worth preserving. 
Such a book becomes a permanent source of interest and 
information for succeeding classes. 

478. Pupils as examiners. — Have pupils prepare 
suitable review questions at home. The abuse of this 
practice seems to be the only valid objection to this 
kind of constructive work. All the general acts in 
the school are tending toward habituation of a desired 
kind, and so there seems to be no good reason why pupils 
should be denied the right to take an active part in mak- 
ing the questions for review or for examination. The 
teacher's supervision is needed at all times, but that is 
no reason for rejecting all the work of this kind. A 
thorough justification may be found in a little actual 
experience. 

479. Class discussion. — Assign topics for discussion 
by individuals. Limit the number so that the whole 
recitation need not be given to this kind of training. A 
few topics intelligently discussed will give variety to the 
exercise and also stimulate a wholesome interest in this 
kind of original research. Do not permit pupils to hold 



GEOGRAPHY 231 

notes while speaking; encourage them to remember as 
much as they can. Have the pupil who is speaking face 
the class. 

480. Debates. — Have debates in grammar grades. 
These debates serve as a valuable kind of review. The 
pupils are required to select the essential facts, to weigh 
them in comparison with other facts, and then to use 
their reasoning powers in defending what they hold to 
be the facts of most importance. The following subjects 
for debate are suggested: Germany vs. United States; 
Limited Monarchy vs. Republic; Eastern United States 
vs. Western United States, taking the Mississippi River 
as a dividing line; Railroads vs. Steamships in the Devel- 
opment of Commercial Prosperity. 

481. Commercial trips. — These trips are journeys 
from one port to another. Their purpose is general 
review. Pupils must name the ports, the steamship 
lines connecting, the cargo, the cities passed, the status 
of respective nations, the favorable or unfavorable 
climatic condition, ocean currents, return cargo, etc. 
Encourage pupils to sketch outline map to indicate the 
journeys made. 

482. Geographical cards. — Many excellent series 
of geographical cards are issued by the various publish- 
ing houses. Some of these cards are intended only for 
review, while others furnish interesting information of 
literary, historic, and scientific value. For personal use, 
teachers can make such cards covering the specific 
work of their own grade. 

483. Competition. — The kind of interest sustained 
by spelling matches and other competitive drills can 
likewise be applied in review in geography. An interest- 
ing application of this kind of drill is the assigning of 



232 METHODS IN EDUCATION 

each child to one country in Europe, for example, and 
then asking him to be ready to present a complete defense 
of all the advantages of his country. The blackboard 
may be divided into sections so that each child may 
write a list of the important points in his defence. 

484. The globe an essential. — Every class in geog- 
raphy should have a globe. Better yet if every pupil 
can have one during certain recitation periods and study 
periods. No child can learn all his geography by per- 
sonal study of the earth itself, and so a globe should be 
made the most useful objective aid in all stages of the 
work in geography. Expensive globes are not necessary ; 
in fact, complex and elaborate representations are con- 
fusing. A large globe can be made of clay, paper, or 
wood. Then paint the surface black and observe the 
advantage and delight in using crayon to illustrate the 
point of the early lessons in geography. , 

485. Uses of the globe. — Following are some of the 
specific uses of the globe in teaching: 

1. Shape of the earth. The earth is an oblate sphe- 
roid. Then show the flattened surface at the poles. 
To carry the suggestion further, illustrate the flattening 
process by whirling a ball of moist dough on a wire or 
rod as axis. 

2. Axis, poles, equator. 

3. Rotation of earth. This will give foundation for 
later teaching of causes of day and night. 

• 4. Revolution of earth. This will lead to causes of 
change of seasons. 

5. Inclination of axis, zones, ecliptic, latitude, longi- 
tude, meridians, and parallels. 

6. Distribution of land and water. Draw line around 
globe and observe which hemisphere has the more land. 



GEOGRAPHY 233 

7. Relative position of continents, countries, oceans, 
seas, etc. 

8. Relief globe for illustrating surface. 

9. Commercial routes to show the world's highways 
of commerce. 

10. Use the globe in every development lesson to 
remedy defective ideas arising from studying a flat 
map. 

486. The shape of the earth. — It is a difficult matter 
for pupils to understand all the facts used to prove that 
the earth is a sphere, but this difficulty is not a valid 
reason for dropping that work altogether. Pupils can 
understand some of the proofs; later in school hfe more 
proofs will seem clear; and during all the geography 
work, the pupils will be making useful inferences be- 
cause they have faith in the conclusion. This topic 
is a valuable one because it invites thought all through 
Ufe. 

Lesson Outline on Shape of Earth 

I. Aim. To prove that the earth is a sphere. 
II. Preparation. The very announcement of the 
aim arouses curiosity. Additional interest may be 
awakened by having a cube, a cardboard disc, a wire 
hoop, a large globe, and a small globe for each pupil. 

III. Presentation. The proofs involve personal 
experience and derived information. 

1. Horizon is always a circle. 

This proof is a matter of observation. It is true for 
all locations. Use wire hoop to illustrate. Take any 
point within hoop, keep hoop in the plane of vision, and 
the limiting line of vision is always circular. 

2. When ships are approaching, masts are seen first, 



234 METHODS IN EDUCATION 

then the lower part of the masts, and finally the whole 
ship. 

This is likewise a matter of actual observation. Illus- 
trate by moving objects on the globe. 

3. New stars come into sight as we reach new latitude. 
This is information from the experience of others. 

Show that this change in the sky may be due to the 
curved surface of the earth. Use pointer held against 
object moved on globe and observe arc described by end 
of pointer. 

N.B. These three proofs simply indicate that the 
earth has a curved surface. 

4. The earth has been circumnavigated. 

This is a fact in history. Recall Magellan's voyage 
from Spain across the Atlantic, through the Straits of 
Magellan, over the Pacific to India, around the Cape of 
Good Hope, and thence back to Spain. That voyage in 
1519 and 1520 was the first complete circuit of the globe. 
Show commercial routes around the world. Show by 
cardboard disc that the circumference is a way leading 
back to any starting point; but a passage over the edge 
of the plane surface of the card would not lead back. 
Recall fear of sailors on first voyage of Columbus. They 
thought they would drop off the flat surface west of Spain 
and never be able to return. 

5. Earth's shadow on the moon in an eclipse is always 
a circle or part of a circle. None but a spherical body 
can cast a circular shadow in any position. 

Illustrate this by holding cube in the sun. Likewise 
with disc, pencil, pointer, book, etc. Observe shadow 
of pupil. The shape of the shadow is like the shape of 
the body casting the shadow. Briefly explain eclipse 
and show pictures of eclipses. 



GEOGRAPHY 235 

6. Analogy. All the other planets are seen to be 
spherical, and it is not probable that the earth is an 
exception. 

This fact about other planets is verified by astrono- 
mers. Use of powerful telescopes is an interesting topic. 

Note. — These are proofs that the earth is a sphere. 
The following proofs are intended to demonstrate the 
flattening at the poles; in other words, the earth is an 
oblfiite spheroid. Proofs 8, 9, 10 should not be given in 
elementary work in geography. 

7. It is a law of all rotating bodies that they rotate 
upon their shortest diameter. If a spherical body in 
a fluid state be rotated, its axis of rotation will become 
its shortest diameter. 

8. By actual measurement of the arcs of meridians, 
it is found that a degree increases in length towards the 
poles. This shows that the arcs near the poles are arcs 
of larger circles. 

9. A pendulum vibrates more rapidly near the poles 
than at the equator. This is due to greater force of 
gravity. 

10. Bodies increase in weight when moved from the 
equator to the polar regions. This is partly due to 
gravity, as in 9. 

IV. Conclusion. The earth is an oblate spheroid. 
Its polar diameter is 26.48 miles shorter than its equa- 
torial diameter. 

Climate 

487. Extension of the term. — The comprehensive 

use of the word climate requires a study of temperature, 

moisture, and all the modifying conditions of each. 

Temperature embraces the variations of heat and cold; 



236 METHODS IN EDUCATIOINJ 

weather relates to daily temperature; climate means an 
average of weather conditions during an extended period. 
Moisture is water in any of its forms. 

488. Conditions affecting climate. — The conditions 
affecting climate can seldom be considered alone; they 
modify one another. Younger pupils cannot under- 
stand all of the facts at first, but later study will utilize 
what is understood in the early lessons. These modifying 
conditions are often studied in relation to causes and 
effects. 

1. Latitude. CHmate becomes colder as distance 
increases north or south from the equator. The region 
of the equator receives the vertical rays of the sun; the 
regions north or south receive heat from oblique rays; 
the polar regions are deprived of heat and light for certain 
periods. This difference in vertical and oblique rays of 
the sun is due to the inclination of the earth's axis. The 
earth's radiation of the heat received is the fundamental 
condition to be considered here. 

2. Altitude. The general rule is that cold increases 
with altitude. Three hundred feet make a difference 
of one degree. Rapid radiation of heat is the principal 
cause. 

3. Proximity to the sea. Effect is toward uniform 
climate; cooler in summer, warmer in winter. The 
sea absorbs heat and radiates heat more slowly than the 
land. Hence, cool breezes from the sea in summer, 
warm breezes in winter. 

4. Prevailing winds. Climate is modified by heat, 
cold, and moisture distributed by winds. Sea breezes 
carry much moisture; land breezes are dry winds. 

5. Position and direction of highlands. Highlands 
modify climate by shutting off hot or cold winds; by 



GEOGRAPHY 237 

condensing moisture till it falls as rain; and by inter- 
cepting moisture-bearing winds. 

6. Slope of country. Note how slope may favor 
climate under each of the five conditions already 
mentioned. 

7. Nature of the surface. Forests equalize tempera- 
ture and prevent droughts and floods. Deserts and 
sandy soils radiate heat rapidly; clay soils retain heat 
and moisture. Large areas of cultivated land absorb 
and radiate heat more rapidly than grazing lands. Bogs, 
marshes, and other lowlands tend to cool the air and 
cause fogs. Rocky surfaces heat and cool quickly. 

8. Ocean currents. See Gulf Stream, Japan Current. 

Illustrations of Climatic Influences 

1. Western Alaska. Inference from latitude and 
altitude, cold; but proximity to sea, warm winds, and 
westerly slope favor mildness of climate. 

2. Newfoundland same latitude as Ireland. New- 
foundland cold by latitude, by Arctic current, by 
prevailing winds; Ireland has warm climate on account 
of Gulf Stream, winds, nature of surface. 

3. The great deserts of Utah and Nevada are caused 
by the position and direction of the Sierras; moisture 
shut off and precipitated. 

489. Forms of moisture. — Since moisture has so 
much to do with climate, it is necessary to consider the 
forms of moisture, their causes, and a particular explana- 
tion of rain. 

1. Water vapor is a name given to moisture in an 
invisible form. Water which passes into the air by 
evaporation may be said to exist as water vapor. 

2. Dew is one form of condensed vapor. If air con- 



238 METHODS IN EDUCATION 

taming water vapor be cooled, the vapor will approach 
saturation, since the lower the temperature, the less the 
capacity for water vapor. On clear, calm nights the 
soil and vegetation radiate heat; the surrounding air 
becomes cooler; hence, vapor is condensed into small 
drops of water. The temperature at which condensa- 
tion occurs is the dew-point. 

3. Frost is frozen dew. Frost is formed when the 
dew-point is below 32 degrees Fahrenheit. 

4. Fog. A visible mass of vapor on or near the 
ground is fog. Condensation is caused by the meeting 
of warm air and cool air. Thus the Newfoundland fog 
is caused by the warm air from the Gulf Stream meeting 
the cool air from the Arctic Current. 

5. Clouds are visible masses of vapor floating in 
the air. 

6. Mist is vapor falling in very small drops. 

7. Rain is condensed moisture which falls when it 
becomes heavier than the atmosphere. 

8. Hail is frozen rain. 

9. Snow is frozen vapor. 

10. Glaciers are rivers of ice. 

11. Icebergs are portions of glaciers broken off and 
floating in the ocean. 

490. Rain. — The four processes requiring explana- 
tion are evaporation, condensation, saturation, precipi- 
tation. 

I. Evaporation. Familiar facts from observation. 

1. Steam is condensed vapor coming from heated 
water. 

2. Heat from the sun or from other sources turns 
liquids into water vapor, and then the water vapor rises 
in the air. 



GEOGRAPHY 239 

3. Water evaporates from clothes hung on a line. 

4. Ink evaporates from wells. 

5. Hands become chapped in spring because winds 
cause rapid evaporation. 

6. Some ponds and brooks dry up in the summer. 

7. Place dish of water in the sun and notice the 
effect. 

8. Roads, sidewalks, and porches dry rapidly after 
a rain. Sun and wind hasten evaporation. 

9. During hot afternoons in summer, the sun can be 
seen '^ drawing water"; i.e., actual evaporation can 
be observed. 

10. Definition. The process of moisture passing into 
water vapor, under the action of heat, is evaporation. 

11. Condensation. 

1. Steam is not strictly water vapor since steam is 
visible. Water vapor, partially condensed by contact 
with cool air, is steam; and further condensation into 
water can be produced by having the steam come into 
contact with cold glass, slate, or other surface. 

2. Moisture from the breath condenses on cool 
window panes. 

3. Moisture condenses on the outside of a pitcher of 
water. 

4. When pupils say they see their breath on a cold 
day, they see only the condensation of the moisture in 
their breath. 

5. Definition. The process of water vapor or other 
forms of moisture passing into water, under the action 
of cold, is condensation. 

III. Saturation. Condensation of moisture in the 
atmosphere is caused by the cool surfaces of forests, 
hills, mountains, or by cool currents of air. Saturation 



240 METHODS IN EDUCATION 

denotes simply the extent of condensation; it is all the 
moisture that the atmosphere can hold. 

IV. Precipitation. When saturation causes the 
moisture to become heavier than the air, the moisture 
falls as rain. This condition is called precipitation. 

Summary for Amplication 

1. Heat of sun converts water into water vapor. 
The greater the heat, the greater the evaporation. 

2. Hot air can hold more water vapor than cold air. 

3. When hot air containing water vapor becomes 
cooler the vapor condenses into clouds. 

4. The clouds become saturated by the uniting of the 
particles of water, and then rain falls as soon as the 
weight is more than the air can sustain. 

5. Rainfall is constant in a belt about five degrees 
wide near equator; periodic, north and south of the 
constant belt; variable, beyond the limits of the periodic 
belts. 

6. Rains purify the air, modify cHmate, clean the 
surface of the earth, and help sustain all animal and 
vegetable life. 

7. Notice the circulation of water: Rains supply 
springs, brooks, rivers, and all other sources of moisture; 
springs, brooks, and rivers unite to supply larger bodies 
of water; evaporation furnishes moisture in the form 
of water vapor for the air; water vapor condenses into 
clouds, particles unite and fall as rain. Think how this 
circulation is a natural way of sustaining the conditions 
required for agriculture, manufactures, commerce, and 
the leisure joys of life. 

491. Glaciers. — This lesson need not be difficult if 
teachers will distinguish known and unknown. 



GEOGRAPHY 241 

I. Preparation. Recall hill, mountain, snow-capped 
summit of mountains; the melting, moving, and falling 
of snow on roofs, hills, and known mountains; successive 
thawing, snowing, and freezing on skating ponds; the 
familiar processes of wetting and packing snow in making 
houses, forts, snow-men. 

II. Presentation. Most of the facts are famihar. 
Larger applications are required. 

-1. Formation. Heavy snowfall on mountains during 
long winters. Summers too short to melt all the snow. 
Year after year snowing, thawing, melting, packing, and 
freezing continue. Thus the immense mass of snow and 
ice is formed into a glacier. 

2. Movement. The slope of the mountain, the thaw- 
ing, and the weight of the glacier will tend to cause a 
movement. Amount, one foot or more in a day. The 
top of the glacier moves faster than the bottom, the 
centre faster than the sides. Why? Tall, narrow 
glaciers move more rapidly than broad ones. Why? 

3. Action of the glaciers. Huge rocks are torn away 
by the sides and bottom of the glaciers. Some of these 
rocks are crushed and distributed as soil, while others, 
badly scratched, are left in the pathway of the glacier. 
Such rocks are found on Long Island and in many parts 
of New England and New York . 

4. Norway, Sweden, Switzerland, and Alaska are the 
homes of glaciers. The western coast of Norway is a 
series of beautiful fiords caused by glacial action. 

III. Drill. Whether named as application or con- 
tinued presentation, this lesson is made more vivid by 
the following. 

1. Pictures of glaciers. 

2. Pictures of fiords. 



242 METHODS IN EDUCATION 

3. Stereopticon views. 

4.' Magazine articles on life in the Alps. 

5. Blackboard drawings. This subject is adapted 
to crayon illustration. 

6. Geography readers and other correlated material. 

7. Allied topics for collateral reading or for future 
lessons: Crevasses and moraines; the Ice Age in North 
America; icebergs. 

492. Icebergs. — See lesson on glaciers. Icebergs 
are parts of glaciers. When the forward part of a glacier 
moves into the ocean, the force of the water lifts up the 
submerged part and breaks it off. This detached mass 
of ice then floats away as an iceberg. Ice is only a little 
lighter than water, and so only one-eighth of the iceberg 
remains above the surface of the water. The course of 
icebergs is directed by winds and ocean currents. Ice- 
bergs cool the temperature, cause fogs, and endanger 
navigation. 

493. The seasons. — Pupils living in the temperate 

zones are familiar with spring, summer, autumn, and 

winter, but many pupils never fully understand summer 

and winter in the frigid zones and wet and dry seasons 

in the torrid zones. A season seems to stand for fixed 

temperature within definite zone boundaries. But as 

climate is the result of many modified causes, so the 

seasons yield to local conditions as we pass from zone 

to zone. 

Facts for Lesson 

1. The sun illumines but half the earth at once. 

2. The earth revolves around the sun once in 365 
days. 

3. The earth's axis is inclined 23J° to the plane of 
its orbit. 



GEOGRAPHY 243 

4. The earth's axis always points in the same direc- 
tion. The north pole points toward the north star. 

5. Temperature depends upon the direction, duration, 
and distance of the sun's rays. 

Inferences 

Different parts of the earth's surface mil receive dif- 
ferent degrees of heat during the year. These differences 
may be stated in describing each of the seasons. See 
geography or drawings. 

Description of Seasons 

1. Spring. On the 20th of March the sun's rays 
are vertical at the equator; the circle of illumination 
intersects the poles; days and nights are equal every- 
where, and h«at is increasing in the northern hemisphere. 
This is the vernal equinox and the season is called spring. 

2. Summer. On the 21st of June the sun's rays are 
vertical at the Tropic of Cancer; the circle of illumina- 
tion extends 23J° beyond the north pole and falls short 
23 J° of the south pole; days and nights are longest in 
the northern hemisphere and shortest in the southern; 
heat is greatest in the northern hemisphere. This is 
the summer solstice and the season is summer. 

3. Autumn. On the 22d of September the sun's 
rays are again vertical at the equator; the circle of 
illumination intersects the poles; days and nights are 
equal as on March 20; heat is decreasing in the northern 
hemisphere and increasing in the southern hemisphere. 
This is the autumnal equinox and the season is autumn. 

4. Winter. On the 21st of December the sun's rays 
are vertical at the Tropic of Capricorn; the circle of 
illumination extends 23 J° beyond the south pole and falls 



244 METHODS IN EDUCATION 

short 23 J° of the north pole; days are longest in the 
southern hemisphere and shortest in the northern; heat 
is greatest in the southern hemisphere. This is the 
winter solstice and the season is winter. 

494. Zones. — Divisions of the earth's surface, cor- 
responding to the amount of heat received and to the 
varying length of days and nights, are zones. 

The lesson on the seasons gives the essential facts 
used in this lesson. This is simply a classification of 
those facts. 

1. Torrid Zone lies between Tropics of Cancer and 
Capricorn. 47° or 3250 miles wide. Torrid means 
hot; this zone is the hottest portion of the earth. 
Days and nights nearly equal. Two seasons, wet and 
dry. 

2. North Temperate Zone lies between Tropic of 
Cancer and the Arctic Circle. 43° or 3000 miles wide. 
Days and nights vary in length. Temperature varies; 
four seasons. 

3. North Frigid Zone is north of the Arctic Circle. 
Width from Arctic Circle to north pole 23J° or 1625 
miles; modern texts speak of the widths as 47°. Oblique 
rays of the sun part of the year. Days vary in length 
from twenty-four hours to six months. Two seasons, 
summer and winter. 

4. South Temperate Zone is bounded by Tropic of 
Capricorn and Antarctic Circle. 43° wide. Four sea- 
sons opposite in time to North Temperate Zone. 

5. South Frigid Zone. Size similar to North Frigid. 
Days and seasons opposite to North Frigid. 

495. Isotherms. — Isotherms or isothermal lines are 
lines drawn upon a map or globe connecting all places 
having the same average temperature. Thus the 



GEOGRAPHY 245 

isotherm of 50° Fahrenheit passes through New York at 
40° latitude and London at 50° latitude, making a dip 
of 10° in latitude. The true climatic zones do not 
correspond to the astronomical zones already discussed. 
The Torrid Zone is bounded by 70° F.; the Temperate, 
by 70° F. and 32° F.; the Frigid is below 32° F. 

It is interesting to have the class follow a few isotherms 
around the earth and ascertain the causes for variation 
in latitude. Such an exercise will apply the facts under 
causes of climate. 

Latitude and Longitude 

496. — A lesson outlined. — This topic is so important 
that it seems prudent to suggest material for class work 
or examinations. 

I. Aim. To understand latitude and longitude as 
means of locating places on the earth. 

II. Preparation. Conversational exercise about 
familiar ways of locating things. Numbers for rooms, 
coat hooks, houses; aisles and rows of seats in the school- 
room; avenues and streets in the city. Show plan of 
regular section of a city where streets and avenues are 
at right angles. None of these ways adapted to earth 
as a whole; hence, necessity for another way. 

III. Presentation. Have circular disc, blank globe, 
maps, and mapped globe. Draw axis and equator on 
circular disc and blank globe. These give starting 
points for measuring. 

1. The name of the equator is known. Measure 
north and south in inches. Show impractical use 
of such standards as inch, rod, or mile. Tell that 
the degree is the unit and that every circle contains 
360°. This number was chosen because it is divisible 



246 METHODS IN EDUCATION 

by all numbers from 1 to 12 except 7 and 11. 
These facts must be accepted; they do not admit 
development. 

2. For latitude, tell that the equator is starting point 
for measurement north or south. Hence, places on 
the equator have no latitude; they are marked 0°. 
Now draw a circle passing through the poles; ehcit that 
the north pole is a terminus in measuring north latitude, 
that the south pole is a terminus for south latitude; 
that the distance from the equator to either pole is one- 
fourth of the whole circle, or 90°; that the limits of 
latitude are 0° and 90°. 

3. Parallels. Lines can be drawn parallel to the 
equator for convenience in indicating latitude. Call 
such lines parallels. Why? 

4. Definition. The distance in degrees north or 
south of the equator is latitude. 

5. For longitude, another starting point evidently is 
required. Tell pupils that the meridian passing through 
Greenwich, England, is the Prime Meridian. Prime 
means first; meridian means midday because all places 
on it have midday at the same time. 

6. Draw Prime Meridian on black globe or indicate 
it on mapped globe. Two kinds of longitude, east and 
west. Have two pupils move objects from Prime 
Meridian east and west around the equator and thus 
observe that the maximum east or west longitude is 
one-half way around the earth, or 180°. 

7. Meridians. Lines are necessary for indicating 
longitude; hence, the meridians. 

8. Varying length of degrees of longitude. Observe 
meridians on globe and maps; mark meridians and cut 
sections from apple, watermelon, or other spherical forms. 



GEOGRAPHY 247 

Make pupils see that greatest length of a degree of longi- 
tude is on the equator; at the poles, 0°. 

9. Definition. Distance in degrees east or west 
from the Prime Meridian is longitude. 

IV. Applications. 

1. Practice in reading latitude and longitude at top 
and bottom of maps. Here explain that meridian of 
Washington is also used. 

2. Find actual latitude and longitude of specified 
cities and countries. 

3. Give latitude and longitude of certain places and 
have pupils find places. 

4. Location of ships at sea. All ships have chro- 
nometers showing accurate time at Greenwich. For 
instance, suppose the sun indicates 10 a.m. when the 
chronometer indicates 3 p.m. Since any spot on the 
earth's surface passes through 360° in 24 hours, each 
hour is equivalent to 15°. The difference in time be- 
tween chronometer and sun is 5 hours, or the equivalent 
of 75°. Hence, the ship is in 75° west longitude. The 
longitude is west because the time by the sun is earlier 
than the time by the chronometer. Reverse the facts 
and the longitude would be 75° east. 

497. International Date Line. — If a man starts 
westward from London to travel around the world, 
he must set his watch back one hour for every 15° passed 
over if he wishes to have .the correct local time. This 
would require twenty-four changes during the journey 
around the world, and thus he will lose twenty-four 
hours or a whole day. 

If he starts eastward from London, he would set his 
watch ahead twenty-four times, and thus he would 
gain a day. 



248 METHODS IN EDUCATION 

To overcome such differences, the nations have agreed 
upon a place where time shall be changed. That place 
is the 180th meridian east and west from Greenwich. 
Suppose the two men start from Greenwich near London, 
one going eastward and the other westward. The one 
travelling eastward will find the time twelve hours later 
than when he started, while the one traveUing westward 
will find the time twelve hours earher. So the latter 
in crossing the line on Wednesday must call the day 
Thursday; while the one travelling eastward in crossing 
the line on Wednesday must call the day Tuesday. 

498. Standard time. — The railroads of the United 
States have agreed upon scheduled places for changing 
time. Following are the divisions: 

75th meridian. Eastern time. 
90th meridian. Central time. 
105th meridian. Mountain time. 
120th meridian. Pacific time. 
It is evident that the difference in time between any 
two of these divisions is one hour. 

499. Volcanoes : Concrete presentation. — One device 
for giving pupils a concept of volcanoes is to observe 
coke, ashes, and iron slag, which are known products 
resulting from the action of heat; to explain the forma- 
tion of the earth by the process of cooling of the surface 
while the interior still remained hot; to make drawings 
to illustrate earth's crust, heated interior, and cracks in 
earth's crust; to show picture of active volcano; and 
to read or give vivid description of the action and results. 
This plan gives the general idea of a volcano without much 
emphasis upon details. 

Another presentation. — This plan involves a scien- 
tific treatment of the topic. In matter and method it 



GEOGRAPHY 249 

is suited to older pupils. Heat of the interior of the 
earth is explained and proved as follows: 

1. Hot springs are evidence of interior heat. Some 
found as far north as Iceland. 

2. Geysers are another indication of interior heat. 

3. Increasing heat in mines. Heat increases about one 
degree with every sixty feet of descent into the earth. 

4. The nebular hypothesis regarding the formation 
of^ the planets explains the existence of the heated 
interior and the cooling crust. In the process of cool- 
ing the contraction causes many fissures, foldings, and 
openings in the crust or surface of the planet. 

Action of volcanoes. Water from the surface of 
the earth passes through the openings into the heated 
interior; the heat expands the water into steam, and 
this added power causes an explosion or eruption. The 
matter thrown out during an eruption is lava, or melted 
rock, pumice stone, water, steam, sand, mud, cinders, 
and ashes. The opening through which the materials 
are forced is the crater of the volcano. 

Noted volcanoes. Mauna Loa and Kilauea in Hawaii, 
Chimborazo in South America, Hekla in Iceland, Etna 
in Sicily, and Vesuvius near Naples in Italy. 

Graphic aids. 

1. Pictures of extinct, dormant, and active volcanoes. 

2. Drawings of vertical section showing base, cone, 
crater; the process of mountain building around crater; 
the contour of the volcanic mountain and the distribu- 
tion of ejected materials. 

3. Maps showing location of principal volcanoes. 

4. Specimens of pumice stone, lava, ashes, etc. 

5. Narration, description, and illustration of the 
destruction of Pompeii. 



250 METHODS IN EDUCATION 

6. Stereopticon views. 

Definitions. A volcano is a mountain or hill, usually 
more or less conical in form, from which lava, cinders, 
steam, sulphur gases, and the Hke are ejected; — often 
popularly called a burning mountain. — Webster. 

This definition is scientifically inaccurate. A volcano 
is not necessarily a mountain; the mountain is the 
result of the accumulation of material ejected by vol- 
canic action. Again, a volcano is not a burning moun- 
tain; the explosion is not a process of consuming material 
by burning. 

A volcano is a hole in the earth's crust from which 
steam, lava, or ashes are or have been thrown. — Dexter 
and Garlick's Object Lessons in Geography, page 155. 

A volcano is essentially a vent in the surface, through 
which rises some kind of molten rock, which, upon 
accumulating, builds a conical peak. — Tarr^s Elemen- 
tary Geology, page 329. 

Illustration of Eruption of Vesuvius 

Large glass vessel, small bottle of red wine, clay or 
sand, water. Form miniature mountain on bottom of 
vessel; make small hole in cork of wine bottle and then 
cover bottle with sand; put water in vessel. When 
ready, stir the water. The water removes sand from 
hole in cork and the wine ascends in a whirhng plume. 
— McKay^s Magic Experiments, page 30. 

500. Winds. 

I. Circulation of the atmosphere. The air is very 
elastic and so it is easily put into motion by changes in 
temperature. Heat causes air to expand, become hghter, 
and rise. This upward current of warm air is replaced 
by heavier cool air which in turn rises after becoming 



GEOGRAPHY 251 

heated. Apply this explanation to the large areas in 
the equatorial regions and notice four great movements 
in the general circulation of the atmosphere: 

1. The inflowing surface winds. 

2. The uprising heated current. 

3. The outflowing winds at high elevations. 

4. The descending air at considerable distance north 
and south of the equator. 

^11. Relation of air pressure and wind. The ris- 
ing column of warm air pushes away the air above it, 
thus decreasing the barometric pressure ; but the reverse 
is true in regard to pressure when the cooling air becomes 
heavier by condensation. Then it follows from the 
last topic that wind and air pressure -ftFe-elosely related. 

501. Trade winds. 

I. The name. The name trade winds is given be- 
cause commercial vessels take advantage of the aid 
given by these winds. 

II. Location. In Atlantic Ocean 8° to 29° N. and 
3° N. to 28° S. In Pacific Ocean 2° to 25° N. and 2° 
to 21° S. latitude. It is sufficient to say about 30° 
north and south of the equator. 

Cause. Cooler air rushing in to replace rising air 
in equatorial regions. See explanation in circulation 
of atmosphere. 

III. Direction. From the northeast in the northern 
hemisphere; from southeast in the southern hemisphere. 
Such incoming air tends to blow from north and south; 
but the earth's surface at the equator is moving east- 
ward at the rate of seventeen miles a minute, and so 
the wind lags behind. 

IV. Effects. 

1. Aid navigation. Columbus followed this route. 



252 METHODS IN EDUCATION 

2. Coming from cold regions, they absorb moisture 
and thus cause deserts. 

3. Absorbing much moisture from the ocean, they 
produce abundant rainfall on sloping coasts. 

4. The meeting of so much warm air at the equator 
produces an upward movement over an area nearly 400 
geographical miles wide. This area is the belt of equa- 
torial calms. 

How to Study a Map 

502. Importance. — This is only one more phase of 
teaching pupils how to study. Lay aside theoretical 
discussion and join a healthy class in studying Asia. 
The response will convince you of the direct value of 
community effort. Here are some of the real conditions 
in an effort of this kind: 

1. Geography is disliked by some pupils because it 
has not been well taught. The pupils have not been 
taught how to use the text-book. 

2. Every pupil has a geography. The ownership 
of the book or the right to use the book is a native 
impulse waiting for invitation to react, according to 
James and Thorndike. The handling of the book gives 
employment to the hands, — another suggestion of free- 
dom from mischief. The coloring of the map appeals to 
the eye. In brief, such presence of material means a 
kind of business that appeals to a healthy class. 

3. The teacher works with the pupils. There is a 
natural interest in such mutual observation, interpreta- 
tion, and discovery; and a derived or acquired interest 
follows for all pupils who experience for the first time 
the joy of finding how much can be learned without 
reading even one line of the text. 



GEOGRAPHY 253 

503. The process of studying a map. — A large globe, 
a map of Asia, a map of the world, and a relief map of 
Asia are ready. Light, heat, ventilation, and comfortable 
position are physical requisites. PreUminary questions 
on globe and maps will secure attention and thereby 
prepare the minds for united and individual effort. 
Such questions will determine comparative location, size, 
and shape; location of highlands and lowlands; general 
direction of mountains and peninsulas. Now turn to 
individual maps; eagerness guarantees activity. The 
map study gives information on these topics. 

1. Actual location by latitude and longitude; land 
and water boundaries. 

2. Size. The largest continent; the largest moun- 
tains, rivers, seas, bays, countries, peninsulas; and, by 
inference, the largest population, forests, animals. This 
inference requires later proof from text. 

3. Surface. The location, direction, extent, and names 
of mountains; the three great slopes as indicated by 
direction of flow of rivers; the names of rivers and the 
bordering waters ; important lakes and seas. 

4. Climate. Probable conditions by comparison with 
North America; apphcation and probable results of each 
of the causes affecting climate. Here, again, is another 
invitation to later use of the text to verify inferences. 

5. Countries and their chief cities; apparent means 
of commercial intercourse. 

6. Industries, products, and commerce. Map study 
alone cannot give the accurate knowledge required, but 
it can correlate old knowledge and also make pupils 
think and justify their thoughts in advance. 

7. The people. Prior information is considerable. 
Note vast extent of lands of the different peoples. 



254 METHODS IN EDUCATION 

Pupils' results from studying the map: 

1. Social pleasure. 

2. Self-satisfaction in progress. 

3. Prior knowledge recalled, applied, correlated. 

4. Desire to study text to verify conclusions. 

5. Consciousness of increasing power in studying. 

How to Study the Text 

504. Difficulties. — There are certain difficulties in 
teaching the intermediate grades and it is well to consider 
first the reasons why pupils do have such difficulties in 
using the text in geography. 

1. Poor teaching. It is a safe rule that says pupils 
should use text-books as soon as books can be used 
advantageously. But notwithstanding this view, some 
teachers do not require pupils to use the books furnished. 
The teachers make notes from the books, write the notes 
on the board or dictate them, have pupils copy and then 
memorize. This plan robs the pupil of his right to learn 
to do by doing; it is a waste of time; it exalts the mem- 
ory; it develops a habit of absolute dependence upon the 
teacher. 

2. Defective books. Some text-books are badly 
planned. Pupils have to search in three or four parts 
of the book to find the required facts. Some books are 
not well arranged. The matter may be found in one 
place, but topics are not given; or, if topics are given, the 
order is neither logical nor pedagogical. Other books 
are not adapted to the capacities of the pupils; scientific 
style, or undue emphasis of causal relations when the 
causes are not understood, or the presentation of a con- 
fusing amount of details. 

3. Inactive pupils. This condition may be largely 



GEOGRAPHY 255 

due to poor teaching and defective books. The pupils 
do not feel a necessity for such knowledge. In the 
section on how to study a map, a way of arousing a 
desire for study of text has been suggested. 

505. The Process of studying the text. — The six 
topics followed in the study of the map make a topical 
series for guidance in studying the text. Whether the 
arrangement of the text is in that order or not, the pupils 
are working under definite aims. The pupils must 
classify the facts under the topics; the efforts must be 
systematic ; and the mental result should be a tendency 
toward a habit of thinking. 

506. Suggestions for the aid of pupils in studying the 
text. 

1 . Pupils must feel the need of the facts in the printed 
matter. 

2. Pupils should have a guide in their study, such as 
topics, questions, etc. 

3. The teacher should work with the pupils to see 
that they acquire proper habits of application and in- 
terpretation. There is too much scattering of energy. 

4. Have pupils read a portion of the text, tell ex- 
plicitly what the author means, and comment upon it 
or otherwise apply it. It is a very valuable exercise 
in observation to have pupils read exactly what is 
printed, give its precise meaning, and then express a 
personal opinion upon it. 

5. Proof. The printed text must disprove or verify 
the conclusion reached in the study of the map. Here 
is authority vs. opinion. Judgment and reasoning are 
required in every complete act in this kind of study. 
The map might suggest the tundras as an inviting home 
for man, but the text describes those mossy swamps as 



256 METHODS IN EDUCATION 

suited only to nomadic tribes who manage to live upon 
fish and fur-bearing animals. 

6. Comparison. The study of North America and 
Europe has habituated pupils to associate climate, 
occupations, and productions according to zones. Such 
types of knowledge are used in map studies; but the text 
must furnish the conclusive facts to enable the pupil to 
ascertain the truth by comparison and contrast. Tabu- 
lated facts in parallel columns give a mode of visualizing 
truth in the field of world geography. As in proof, here, 
too, the text must be used for accuracy. 

7. Synopsis. Critical study of the printed matter 
is insisted upon in each of the foregoing suggestions, 
Another means of mastering the text is analysis by out- 
line. The value of this exercise is fully presented in 
the chapter on composition. 

8. Abstract. Another way of making the thought of 
another a part of one's self. See chapter on composi- 
tion. 

9. The text is a source of information for individual 
discussion and class debates. 

507. Characteristics of modern text-books. 

1. Enrichment; physiography. 

2. Pertinent illustrations. 

3. Unit areas vs. unrelated facts. 

4. Heuristic questions. 

5. Inductive development. 

6. Political and industrial relations exalted. 

7. Topical arrangement. 

8. Causal series, cycles, comparison. 

9. Types as apperceptive bases. 

10. Correlation with science, history, and literature. 



CHAPTER XIII 
HISTORY AND CIVICS 

508. An institutional subject. — Butler and Spencer 
have advocated institutional training as a desirable 
preparation for life. John Dewey, Horace Mann, and 
others have come out strongly for citizenship as a worthy 
ideal. The subject-matter of history and civics is com- 
ing more and more into use as suitable means of helping 
pupils toward the ideals advocated by leading educators. 
The suggestions quoted in the following eight sections 
are pertinent. 

509. Early work in history. — In the lower elementary 
grades, topics introductory to history will be found in 
the fables and myths and in literature and geography 
lessons. As pupils in the earlier years take an intense 
interest in events associated with life and endeavor, the 
subject-matter of the lessons in history should be chiefly 
biography and the record of events which have visibly 
shaped or influenced the destinies of man. Only a brief 
sketch of each topic is expected; no notes should be 
dictated by the teacher; no home study should be re- 
quired of pupils in grades below the eighth year. The 
reading of library books should be encouraged. 

510. Geographical background. — The teacher should 
see that pupils have a proper geographical background 
for all historical events. Appropriate use should be 
made of pictures, reference books, and maps to give a 

257 



258 METHODS IN EDUCATION 

fit setting to the narratives, to show the pohtical and 
physical boundaries, to indicate territorial growth and 
expansion, and to illustrate the progress and purposes 
of movements in warfare. The judgment of the pupil 
should be exercised in tracing the causes as well as the 
progress and outcome of great historic movements. 

511. Current events, anniversaries, excursions. — 
Attention should be given to current events and to his- 
toric anniversaries, as Lincoln's Birthday, Washington's 
Birthday, Decoration Day, Independence Day, and 
Thanksgiving. In order to make the subject of history 
real and vivid, pupils should be encouraged to visit the 
Metropolitan Museum of Art, the American Museum 
of Natural History, the museum of the Brooklyn Insti- 
tute, the historical and general libraries. 

Civics 

512. Members of society. — Pupils should be taught 
in all grades, as far as they may be made to understand 
their responsibihties and privileges as members of 
society, and that as such they owe duties to the school, 
to the family, to the neighborhood, to the city, the 
state, and the nation. In this way they may be led 
to comprehend the principles of government and their 
individual duties in connection with it. The necessity 
for obedience to authority should be dwelt upon, as 
also the moral obligation of working with the various 
departments of the government and not against them. 
Wherever possible, the reasons for conduct should be 
explained. If the child knows the reason for any law, 
he will obey that law more readily. 

513. Topics for discussion in all grades. — In all 
grades there should be frequent discussion under these 



HISTORY AND CIVICS 259 

headings: Obedience to law; Why laws are made; Who 
makes the laws? Who enforces the laws? Why are 
law-breakers punished? 

514. Importance of local ordinances. — Principals and 
teachers are urged to lose no opportunity to impress 
upon pupils the importance of city ordinances that are 
specially applicable to local conditions. Pupils should 
be led to see that even slight departures from the stand- 
ard of order and good administration become very 
serious matters when many persons engage in them, 
and that, therefore, each individual should be careful 
to avoid acts, such as throwing paper and fruit skins 
into the streets, which, though trifling in themselves, 
would, if they became general, tend to impair the clean- 
Hness and health of the city. In teaching the ''duties 
of citizens and public officials," special attention should 
be directed to the work of the departments that come 
under the immediate observation of pupils. 

515. Government by the people. — In the higher 
grades of the elementary course pupils should be led 
to appreciate the force of Bryce's statement that ''the 
greatest problem that free peoples have to solve is how 
to enable the citizen at large to conduct or control the 
executive business of the state." It is very important 
that all young people should be made to understand that 
in this country government is not something apart from 
the people, but that it is established by the people them- 
selves, and that there are orderly ways provided for 
giving effect to the will of the people. 

516. Aim of history and civics. — The educational 
aim of civics as of history is to give a body of ideas and 
a trend of action that will assist the child to become an 
intelligent and a patriotic citizen. 



260 METHODS IN EDUCATION 

John Fiske says: " The child should be so trained that 
he will always retain something of interest in reading 
history, something of power in following up a line of 
ordinary investigation, something of a disposition to 
seek for the underlying causes of events, something of a 
grasp of the mighty tendencies and movements of his- 
tory, and some inkling of that conception of history that 
makes it a teacher of the present out of the wealth of 
its past." 

517. Result sought. — First, to make the present full 
of meaning by showing pupils its origin in the past, to 
help them properly to understand the present, to develop 
truth, reason, and high ideals. Second, to develop 
patriotism by causing the pupils to feel a responsibility 
in preserving and upholding the institutions founded by 
their ancestors. Along the line of patriotism is habitua- 
tion to civic requirements. 

518. Habituation to civic requirements. — In discuss- 
ing the ideals of education, citizenship is mentioned as 
one advocated by Horace Mann and John Dewey. For 
those who do not wish to consider education a prepara- 
tion for the hereafter, the ideal of citizenship furnishes a 
satisfactory standard for effort; and for those who wish 
to make the supreme aim of education a preparation for 
the life to come, the ideal citizen may be considered one 
whose hving in this life is a good preparation for the 
hereafter. The teacher who can influence his pupils to 
habituate themselves to adapt themselves to the require- 
ments of the community in which they live, is doing all 
that can be expected from him under the general pur- 
poses of history and civics. 

519. Definition of history. — Locke says that " His- 
tory is the science of the development of men in theii' 



HISTORY AND CIVICS 261 

activities as social beings." A German writer calls 
history ''the politics of the past, and poHtics the 
history of the present." Mace (page 9) says: ''His- 
tory deals with the life of the people in the process 
of growth." 

520. Value of the study of history. — While we have 
not thought it necessary to mention specific values of 
the subjects since all the subjects are deemed worthy 
of places in the course of study, special mention should 
be made of the ethical, patriotic, and practical value of 
history rightly taught. The ethical value may be 
chiefly derived from the study of the lives of great men 
as taught to children. See section 524. The patriotic 
value has been alluded to in section 516. Probably the 
consensus of opinion has established patriotism as the 
important reason for the study of history. This may 
be awakened by striking events which appeal to a pupil's 
feelings, illustrations of the beauties of one's country, 
deeds of illustrious men, the early struggles of the people, 
victories both military and civic, so that the pupil will 
have a pride in belonging to a country which has so 
many claims on his admiration. The natural interest 
awakened by historic places, buildings, scenes of battles, 
and peace conferences develop a love for the past so 
that these future citizens, in the changes which must 
necessarily come to a progressive country, do not lightly 
relinquish the old, for the new. 

Its practical value lies in the fact that history runs on 
in much the same channels that it has with the Anglo- 
Saxon race for hundreds of years. We touch the history 
of our fathers in all present-day national questions. 
Therefore as Bourne (page 81) says, ''The surest road to 
a comprehension of our country, its institutions and its 



262 METHODS IN EDUCATION 

relations to the world lies through history." It intro- 
duces pupils to the world of men and makes them ac- 
quainted with motives and actions. In its different 
phases, its pohtical is represented by the government, 
its religious by the church, its educational by the school, 
its industrial by the occupations, its social by the family. 
The pupils are shown how great movements have been 
made and the effect of these. For the more thorough 
understanding of the present, they must know the past. 
By this knowledge their own judgment is exercised in 
regard to present questions. 

521. The historical sense. — The historical sense is 
not a sixth ''sense," nor a ''faculty"; it is simply a 
feeling that the past can be rightly interpreted only 
when the student lays aside his own prepossessions, and 
seeks in the past itself a means of understanding the 
forces which moved the men of a bygone age, and when 
he enters sympathetically into the spirit which gave 
dignity to their institutions. — Bourne, The Teaching of 
History and Civics, page 9. 

A fully developed character, such as is the aim of all 
education to inculcate, is lacking in one rich field, if it 
does not feel that historic sense which causes respect for 
past institutions and even places of historic note, though 
these may no longer be useful. The nation's historic 
sense, as shown in Holmes's Old Ironsides, was mani- 
fested in its opposition to the destruction of the battle- 
ship Constitution in 1833. 

522. Extent of history. — In the elementary school, 
a good rule is to cover the history of our own country 
and as much of the history of other countries as affects 
our own. This is not a narrow view. It embraces a 
general knowledge of Enghsh history, some French, a 



HISTORY AND CIVICS 263 

little German and Spanish history, and some reference 
to the history of other countries. 

523. Method of teaching history. — Here again we 
face the problem of classifying ways or processes, as 
already discussed in chapters VII and VIII. Perhaps 
the easiest mode of adaptation is to conform to the 
suggestions and plans of approved text-books in his- 
tory and civics until the effort of educators can secure 
for history the uniformity that has been secured for 
geography. Bourne's The Teaching of History and 
Civics is authority on methods. His liberal encour- 
agement to teachers is illustrated when he says, page 168, 
if the teacher ''can succeed in leading his pupils to 
study historj^ to comprehend it, to acquire the habit 
of reading historical literature, his method is sound." 

524. Method in the lower grades. — The study of the 
hves of particular men, in connection with the different 
events in their careers, has been found a fascinating 
source of interest in history. This is especially true in 
the lower grades where most of the history is taught 
biographically. In regard to this, two hints may be 
given. One which does not detract from the interest 
in the grade and which is a benefit in the higher grades 
is this: Teach stories in regard to noted men and the 
events which group themselves about these men in 
chronological order. The second is an exception to the 
first, but it suggests itself because of the interest which 
naturally attaches to it: Teach an event upon the anni- 
versary of the day when it occurred. The work of the 
fifth and sixth years would naturally be to put together 
events, or men and events, to recognize that there is a 
relation between these, and to build a skeleton into 
which later knowledge may be fitted. 



264 METHODS IN EDUCATION 

The worth of biography is well expressed in Foote and 
Skinner's Explorers and Founders of America from 
which book these ideas are taken. The story of a na- 
tion's progress is largely written in the lives of its great 
leaders, and if we wish to create in boys and girls an 
interest in history and in historical reading we must 
appeal to their love for life and action. Great leaders 
exemplify in themselves the ideals and purpose of the 
people whom they lead, and through a study of their 
lives young people may come to know something of the 
causes which make for national success or failure. 

A good example of a great leader will lead the class 
to see in him our country's progress. 

All the religious zeal, the self-denial and the devotion 
to duty, which characterized the era of colonization and 
settlements is told in the lives of founders and the early 
leaders of the colonies. Customs and manners may be 
gained from study of characters. 

If associations are carried on in this way, the child 
will have some appreciation of the causes which led to 
the industrial and social development of a great people, 
some quickening of imagination, and some admiration 
for courageous perseverance in the face of difficulties 
and some respect for duty. If we kindle these qualities 
of mind and heart, we shall make our children good citi- 
zens and lead them to see that they can make their 
lives sublime. 

525. The teacher's preparation. — The ideal teacher 
of history is one who has been especially trained for 
this work. Unless a teacher has a broad view of his 
subject and can grasp the whole situation, as a teacher 
of many subjects cannot do in all of them, the proper 
relation of parts cannot be well maintained. But it is 



HISTORY AND CIVICS 265 

possible for every teacher to be reasonably well pre- 
pared, and for this purpose a brief plan is suggested. 

Take any good text-book like Fiske or Gordy for the 
United States. After a thorough reading, note the 
periods into which, in your own mind, the history natu- 
rally divides itself. Compare your own impressions with 
some good outline, such as Kingsley's or McLaury's, 
and then decide upon a composite outline for class use. 
T^ke whatever period is to be studied and subdivide it 
before you conduct the recitation. Two illustrations 
are given. 

Illustration I. Revolutionary period. 

1. Causes which led up to this. 

2. Objects of British. 

(a) To separate the colonies. 

(6) To cut off colonies from the south. 

3. How this was accomplished. 

Under each of these large divisions there would be 
several subdivisions. 

Illustration II. Under the large topic of the Period 
of Settlement are several subdivisions. One of these 
is The Settlement of Rhode Island. 

1. Purpose of Settlers. To found a place of refuge 
for those w^ho suffered religious persecution in Massa- 
chusetts. 

2. Chief Settlers. 

(a) Roger Williams. Founder of Providence. 
Banished from Massachusetts because of religious 
views, — separation of church and state and that no 
one should be obliged to support the church. 

(h) Anne Hutchinson. Founder of Portsmouth. 
Banished from Massachusetts because of religious 
views. 



266 METHODS IN EDUCATION 

3. Government. 

(a) Obtained a very liberal charter from the King 
similar to that of Connecticut. 
(6) Perfect religious freedom. 

A caution to be observed is to keep your bearings. 
Do not let detail lead away from the large theme. If 
time is limited, an outline already prepared may be 
used. Do not make it dead by mathematical precision, 
but let the human element, the feeling in regard to 
eventS; make it mean something and keep it alive. 
Beyond this, in order to intensify his interest and make 
his subject real, the teacher should read at least one 
of the original historical documents, as Bradford's His- 
tory of the Plymouth Colony, or Sources relating to the 
Norse Discovery of America. These may be found in 
any well equipped library. The teacher will feel fully 
repaid for the reading by the power he feels in teaching 
a subject which he knows from the original documents, 
and will realize the practical value because it furnishes 
one criterion for the selection of text-books which are 
true to facts. 

526. Topical method. — This method would be the 
one naturally followed by a teacher whose preparation 
has been similar to that just described. It is necessary 
for the guidance of the teacher to have at least a plan of 
work for the term mapped out by topics. 

The supreme value of the topical method is exempli- 
fied in the work in history. 

One view of this method presents a whole lesson under 
a series of topics arranged in logical or chronological 
order. These eight or ten topics, for instance, furnish 
a guide to whatever the pupil is expected to do in that 
recitation. Another view of the topical method selects 



HISTORY AND CIVICS 267 

one general topic for the subject of the recitation and 
then there are a few subordinate topics assigned to be 
covered in the various ways of conducting the recitation. 
One topic may be set for oral or written review; another 
may cover the required work in collateral reading; 
another may be for general discussion to develop the 
pupil's power of expression and his sense of sound judg- 
ment; while another may be the direct preparation for 
the work of the succeeding days or weeks. Whatever 
the arrangement of the topics may be, the aim should 
be definite assignment, to direct pupils toward what 
they should try to learn, where they may find informa- 
tion, and how they may make that information a part 
of their own mental possession. 

527. Text-book method. — Here again we must dis- 
sent from the adverse criticism of the use of text-books. 
The text-book is the source of information for every 
pupil, and no teacher has a right to deprive the pupil 
of his right to use his own activity in the field of educa- 
tion, nor can any teacher take the place of an accepted 
text-book in this or any other subject. More adverse 
criticism of text-books is not needed; some devotion to 
the ideal in teaching pupils how to study a text-book 
is what is needed. To attain this ideal the teacher 
-should be the master of the text-book, not a slave to it. 
In this as in the topical method important events are 
to be emphasized, and minor details and connecting 
events omitted altogether or kept in proper perspective. 
Doubtless the best results can be secured by a combina- 
tion of these two methods. The text-book is certainly 
necessary even though the topical method be used. 

528. Source method. — The source method of teach- 
ing history, as the word source implies, requires students 



268 METHODS IN EDUCATION 

to consult the original documents from which history is 
written, and then form their conclusions upon that 
material. This method applied in the elementary 
schools would be presented in a text-book not in narra- 
tive form, but in the form of summaries, tables, and 
brief reproductions of the original documents. For 
elementary pupils, this method cannot be commended. 
The pupils lack the foundation knowledge for forming 
an opinion on the material furnished and, besides, they 
have not yet acquired habits of study that will enable 
them to interpret the materials without a great deal of 
collateral reading. The collateral reading in connection 
with an authorized text-book in the class may introduce 
the pupils to the source method in some lines of investi- 
gation. Selections read by the teacher from original 
sources serve a twofold purpose; they put that life 
into history which can only result from making it real, 
and they introduce children to the field of original 
sources. Selections from the following are of especial 
interest to pupils of United States History in the seventh 
and eighth years: Beverly's History of Virginia, and 
Josiah Quincey's Figures of the Past. As the study of 
history in the elementary school is not supposed to be 
intensive, only a mere introduction to source literature 
is all that can be recommended; otherwise, the regular 
work of the course would be neglected. 

529. Collateral reading. — " The object of collateral 
reading is twofold: it supplements a text-book, giving 
the student additional information and describing the 
same events from new points of view; and it also cul- 
tivates the student's interest in history as literature." 
This is Bourne's opinion as stated on page 158. Gordy 
advises the use of a short list of good references rather 



HISTORY AND CIVICS 269 

than the reading of many books. He advises that each 
pupil read one good reference book in addition to the 
text-book. Probably many teachers have noticed the 
shock that a young pupil experiences when for the first 
time he finds text-books disagreeing. This is an oppor- 
tunity to make him realize that books are written by 
men; that in the main historical points men agree; but 
that in minor details the author may give his own point 
of view, or present information that is not authoritative. 
Another advantage derived from collateral reading is 
the skilful use of books. Too many pupils in the elemen- 
tary schools are entirely helpless if asked to look up a cer- 
tain topic. History offers a greater opportunity than any 
other subject for practice in getting definite information. 

530. Open text-book recitation. — ''An excellent sug- 
gestion is that of 'open text-book recitations/ in which 
with their books before them, pupils are asked questions 
on cause and effect, on relations with previous lessons, 
etc.; answers may, if necessary, be written out and 
corrected in class. Such an exercise trains pupils to 
take in the thought of a printed page, and to grasp the 
essential points. 

"Such a system tends to encourage the habit of 
applying what one knows to a new problem. Still more 
helpful in the same direction are the off-hand discussions 
and impromptu debates which spring up in an eager 
class, and which should be encouraged by every good 
teacher." — Committee of Ten. 

531. Cause and effect. — Whatever the method of 
recitation may be, the training of the judgment will 
require pupils to trace the relations between cause and 
effect in all the great events of history. See causal 
series in geography, section 459. 



270 METHODS IN EDUCATION 

Events are meaningless without their settings. The 
cause, the event, the effect are what arouse interest, 
demand thought, appeal to reason and judgment. 

532. What should be memorized. — '' How far should 
pupils be expected to memorize? 'A few things should 
be learned by heart and, when forgotten, learned again, 
to serve as a firm ground-work upon which to group 
one's knowledge: without knowing the succession of 
dynasties, or of sovereigns, or of presidents, or the dates 
of the great constitutional events, the pupil's stock of 
information will have no more form than a jelly-fish.' 
But those few necessary facts ought to be clearly defined 
as only a framework to assist the memory." — Com- 
mittee of Ten. 

Taking an application in United States history, we 
suggest that pupils learn thoroughly the names of the 
presidents with dates of administrations and the political 
party to which each belonged. In the study of the 
constitutional period, this will be found to be indis- 
pensable as a framework for all important facts of recent 
history. The learning of long lists of dates is no longer 
considered a legitimate part of history. The memoriz- 
ing of particular dates in relation to epochs or periods 
is all that is essential, with one or two others which mark 
the important event in some movement. The dates 
which are learned should be learned accurately. Gordy 
says dates are valuable in giving perspective to reveiw 
work. 

533. Verbal repetition. — It is not necessary to give 
much space to reasons why verbal repetition of the 
matter in the text is not the way to teach history. This 
kind of recitation is the cause of severe criticism against 
•the teaching of the past; but a little experience with 



HISTORY AND CIVICS 271 

teachers of this decade leads to a commendation of their 
tact and judgment in matters of this kind. Only poems, 
national songs, and prose selections, which have been 
written with reference to some historical event, are to 
be committed to memory for verbal repetition. 

534. Correlation. — Correlation with geography has 
already been mentioned. Literature is another study 
that can contribute a large share of interest and use. 
Masterpieces in poetry and prose often present the facts 
of 'history under the charm of literature. Lincoln's 
Gettysburg Speech is an apt illustration of the correla- 
tion of oratory and history. 

''The teaching of history should be intimately con- 
nected with the teaching of English: first, by using 
historical works or extracts for reading in schools; 
second, by the writing of English compositions on sub- 
jects drawn from the historical lessons; third, by com- 
mitting to memory historical poems and other short 
pieces; fourth, by reading historical sketches, biographies, 
and novels, outside of class work." — Committee of Ten, 
page 164. 

535. Reviews. — Our point of view was expressed in 
a general way in section 134. That view has particular 
application to history. Good teaching will require a 
summary at the close of each recitation; the assignment 
of home study will be largely a matter of review rather 
than advanced preparation; the making of outlines of 
the matter covered in the regular text or of the matter 
in collateral reading is another valuable exercise; and 
extemporaneous speaking upon assigned topics or brief 
written summaries during the recitation period will tend 
to systematize the whole work under some comprehen- 
sive plan of presentation. 



272 METHODS IN EDUCATION 

As.de from this daily review, when a period has been 
covered it should be given a general review in order to 
see that the pupils hold the subject as a unit and also 
to strengthen the impression. This review should not 
be a restudy of the subjects as presented in the original 
lessons but should be attacked in a fresh way. This 
will avoid loss of interest and help the pupil to organize 
his knowledge more thoroughly. 

Illustration 

After the completion of the study of the Civil War 
take up the history of slavery. This has already been 
studied in connection with the period of colonization, 
in the provision for the non-interference with the trade 
until 1808, in the effect produced upon it by the inven- 
tion of the cotton-gin, in the Missouri Compromise, 
and in the question of whether new states should be 
admitted as slave or free. In the review, let slavery 
be taken connectedly. For such a review excellent 
results can be gained by the preparation of outlines by 
the pupils. 

Gordy suggests three kinds of reviews: 

1. Reviews may be chronological, but must connect 
and associate each one with some important event. 

2. Reviews may be biographical. Noteworthy events 
may be associated with the names of men. 

3. Reviews may be geographical when association of 
events is to be with places. 

Topical reviews are thus defended in Cornman and 
Gerson's Topical Survey of United States History: 

" Sound psychological and pedagogical consideration 
demands that this review should not consist of mere 
repetition, but should, as far as possible, be presented 



HISTORY AND CIVICS 273 

in a fresh guise, and aid the pupil in organizing the 
knowledge which he has already acquired. The various 
elements of the matter to be reviewed should be closely 
interrelated, essential features emphasized, and a broader 
range of view disclosed, so that the knowledge as a whole 
may form an apperceptive system to which future 
acquisition may be readily related." 

536. Use of outlines. — This plan is advocated as one 
of the best means of teaching pupils how to select and 
CQinprehend the essential points in the printed text. 
It is difficult at first, and needs the personal direction 
of the teacher; but a little practice in it gives a con- 
sciousness of growing power so that the pupil will soon 
be anxious to follow this kind of individual work. Out- 
hnes prepared for guidance in study would, of course, 
obviate the making of similar outhnes by the pupils. 
Teachers differ in their views of the value of such out- 
lines in connection with the study of advanced lessons, 
but there is almost unanimous opinion in favor of the 
outhnes in reviewing a part or the whole of a subject. 
Cornman and Gerson's Topical Survey of United States 
History is excellent for reviews. 

537. Note-books. — Elaborate notes are not useful to 
the elementary pupils. The mere copying of long ex- 
tracts is not a prudent investment of time or energ}^ 
Use note-books for the following purposes: 

1. Summaries of work. Similar to that described in 
sections 525, 526. 

2. Progressive maps. 

3. Review questions or topics. 

4. References in connection with collateral reading 
that appeal to the owner of the book. 

538. The use of maps. — The geographical maps are 



274 METHODS IN EDUCATION 

absolutely necessary to fix the location of the principal 
places studied in history. This is one means of corre- 
lating history and geography. One caution to be ob- 
served is that the map shall not have too many places 
located upon it. Confusion must be avoided. 

539. Progress maps. — A helpful means of stimulat- 
ing visualization is the use of progress maps. Outline 
maps can be secured from publishers and so pupils need 
take no time in marking the limits of latitude, longitude, 
and boundaries. That part of map-drawing has httle 
educational value. The progress map will then contain 
the location of the few principal points under considera- 
tion. Thus in the study of the early years of the Revo- 
lutionary War the map will have the location of Boston, 
Saratoga, New York, Princeton, Trenton, Philadelphia, 
and Yorktown. A line may indicate Washington's 
route across from Long Island up the Hudson and then 
down through New Jersey. 

540. Debates. — History furnishes material for the 
frequent use of short debates. The value of such exer- 
cises is evident to all experienced teachers. 

541. Questions prepared by pupils. — This plan of 
promoting self-activity and co-operation has been em- 
phasized, from time to time, in this book. Personal 
experience is the justification for such commendation. 
Gordy, in his notes To The Teacher, says: " The pupils 
should be required to prepare a written question on 
every lesson. The value of this simple device in leading 
them to note the working of cause and effect cannot 
easily be measured. If pupils have not been trained to 
ask such questions they may at first be diffident about 
it. They will also ask questions that call for yes or no 
or for single-word answers. With a httle judicious help, 



HISTORY AND CIVICS 275 

however, they will soon begin to ask searching questions 
that will stimulate the interest of the entire class." 

542. The use of illustrations. — The word illustra- 
tions in this topic has reference to the pictures or other 
illustrations in the text-book itself. One essential of 
any good text-book is that it shall not be overloaded 
with details. So, too, of the use of pictures. The 
illustrations are intended simply to strengthen the 
matter already given in the printed text. The limit to 
be- observed is the truthfulness and the usefulness of 
the illustrations inserted. 

543. Collection of prints and pictures. — In speaking 
of school decorations we advised the use of a few superior 
paintings in place of a large number of cheap prints and 
pictures. The same caution may be applied to history. 
It is suggested that a large scrap-book be used for keep- 
ing the prints and pictures instead of posting them on 
the walls of the schoolroom. 

544. Excursions. — Fortunate is the school that is 
located within the field of historic experience. Excur- 
sions under the plan described for teaching geography 
cannot fail to produce satisfactory results in impressing 
the facts through the aid of concrete interest. 

545. Dramatization of historic events. — Teachers 
can hardly be expected to put the historic material into 
dramatic form for presentation in rhetorical exercises, 
but it is possible to secure such material already drama- 
tized. Such exercises in school will be found one of the 
most valuable means of promoting a healthy school 
spirit. A little play called the Continental Congress, 
in which pupils take the parts of those who adopted the 
Declaration of Independence, may be mentioned as an 
illustration of this phase of the work in history. 



276 METHODS IN EDUCATION 

546. Use of mnemonics. — Anything so artificial is 
not approved as a method of teaching; but it is a device 
that may have some value for some pupils. The follow- 
ing illustration suggests an ingenious and helpful way 
of remembering the events connected with slavery agi- 
tation. 

Notice that the first letters of the seven lines spell 
slavery. 

Sixteen hundred nineteen — Introduced 1619. 

Law prohibiting slaves imported — 1808. 

Admission of Missouri — 1820. 

Violent opposition to annexation of Texas — 1845. 

Emancipation Proclamation — 1863. 

Rebellion the outgrowth — 1861-5. 

Year of 1865 — Thirteenth Amendment. 

547. How to arouse interest. — The summary of the 
last tw^enty-six sections will present a number of points 
of view on the teaching of history. A condensed expres- 
sion of the substance of these points of view will give 
the means of arousing interest in teaching the subject 
to elementary pupils. 

548. Civics. — This is part of the life of today. At 
a very early age the child comes into contact with civil 
government. Just as in the study of history, first he 
learns disconnected facts in regard to city government, 
also in regard to home and school laws, election, taxa- 
tion, political parties. In the seventh and the eighth 
years these isolated facts are gradually brought together 
in a whole represented by the national government. The 
laws of state, county, town, city, school, and family are 
fitted into this whole. 

549. Local government. — The study of the forms 



HISTORY AND CIVICS 277 

and uses of local administration is a part of the early 
work in all the grades in New York City. It is what is 
called institutional presentation of history and civics. 
To impress the utility of such government, many of the 
schools have adopted forms of pupil self-government to 
represent the departments in the larger municipal organ- 
izations. Wherever the school may be, it is possible 
for pupils to study the government related to them. 

550. Process of legislation. — Another means of 
increasing civic knowledge is for pupils to make a special 
study of the three departments of government in the 
state and in the nation. The history of a bill from the 
time that it is introduced until it has been under judicial 
approval is one of the valuable topics in relation to his- 
tory and civics. Turning the class or the school into a 
legislative body for this purpose is one concrete method 
of presenting the work. 

551. Institutional study of history and civics. — In 
the five kinds of inheritances mentioned in Butler's 
definition, the institutional inheritance is found. The 
American tendency is strongly in favor of such training. 

552. Common mistakes in teaching history and civics. 

1. A pupil sometimes receives a good mark because 
he is a fluent talker, rather than because he knows and 
can connect facts. History offers many avenues to 
inaccuracy and a teacher must be constantly on his 
guard. 

2. Past events are kept in the past. Make them 
real by bringing out how they touch the fife of today. 

3. Events are often left hanging in space. This may 
be avoided by the use of maps, by connecting events 
either logically or chronologically, and by giving atten- 
tion to periods of time. 



278 METHODS IN EDUCATION 

4. Indefinite assignment of lessons. This may be 
avoided by the use of topics with their subdivisions. 

5. Too much prominence given to wars. Many great 
questions are fought out and decided in times of peace. 

6. Taking sides. State facts. Do not warp the 
judgment of pupils by such strong partisanship that 
they believe that England had no excuse for the attitude 
she assumed toward the American colonies before the 
Revolutionary War, that the southern people were all 
rebels in 1861, and that the north contained all the men 
of principle. Views sufficient to arouse interest and 
enthusiasm should be given, but proper justice to both 
sides should be shown. 

7. Making the study too critical. It is not necessary 
to spoil the enjoyment of and perhaps decrease the inter- 
est in history by raising a doubt as to the truth of a 
likely story. History should not be studied critically 
in the elementary school. 



CHAPTER XIV 

READING 

553. Value. — Excellence in all other branches of 
school work is dependent upon ability to read well, and 
hence the basic importance of reading. But aside from 
its importance in the acquisition of knowledge in school, 
reading is a means of pleasure for ourselves and others 
during later life. Appreciative reading of good Hterature 
gives strength and refinement to character, and assures 
continued development of intellectual power through 
the use of the mental faculties. 

554. Characteristics of books formerly used. — The 
use of the terms old education and new education is 
indefinite, partly because there is no distinct dividing 
line and partly because the former term is frequently 
associated with adverse criticism. A condemnation of 
the old is a popular argument for the new. It would be 
nearer the spirit of true teaching, however, to give full 
credit to the achievements of the past by using those 
achievements as a foundation for progressive develop- 
ment. There is nothing in matter or method that is 
entirely new; and surely child nature is the same, but 
we understand it better. Adaptation is the mark of 
modern improvement. 

In speaking of the old and the new books in reading, 
there are differences which can be precisely stated. The 
old books had selections possessing intrinsic merit, but 

279 



280 METHODS IN EDUCATION 

the selections taken together did not make a unified 
whole. They lacked that continuity that is deemed 
essential for persistent development. The books were 
compilations of unrelated and unclassified fragments. 
Following is a summary of the leading characteristics: 

1. Graded words and exercises without reference to 
content. 

2. Moral stories. 

3. Information readers. 

4. Patriotic selections. 

5. Literary masterpieces. 

555. Complete works vs. selections. — The accepted 
point of view is quoted from an approved answer in a 
recent English examination. 

''Another reform of great consequence has taken place 
during the past fifteen years in the teaching of reading. 
The movement had its origin in the conviction on the 
part of President Eliot and others that reading was too 
formal; that reading is but a means and not an end, 
and that so soon as the mechanical elements are mastered 
it should be used as a vehicle to transmit the contents 
of literature to the child. This reform, which was 
greatly assisted by the discussions and reports of the 
'Committee of Ten' and the 'Committee of Fifteen,' 
has revolutionized the school readers and the courses 
of study throughout the length and breadth of the land. 
Courses of study in the elementary school now demand, 
in the upper grades, the critical and appreciative study 
of masterpieces of literature, and the school readers are 
no longer made up of ' useful information ' and twaddle 
on moral subjects invented by the compilers of readers. 
But they contain, even in the lowest numbers, pieces 
that possess genuine literary merit. So that instead 



READING 281 

of reading about Janets Doll and Jack^s Top, the boys 
and girls of the second and third grades read the 
poems of Longfellow, Field, and Gary. 

In the secondary and collegiate courses similar changes 
have occurred. Formerly, courses in literature consisted 
largely of the mastery of treatises about literature and its 
creators. Now they consist of the concrete, first-hand 
study of entire masterpieces representing authors or 
types of literary form. 

The changes may be summed up by saying that the 
courses in English have been infinitely enriched by 
placing the emphasis on the subject-matter of literature 
rather than on the mere form of mechanical aspect. " 

556. Guiding principle today. — The one great prin- 
ciple that determines correct methods of teaching read- 
ing is from the whole to its parts. This principle is applied 
all through the elementary grades. 

557. Types of reading matter used at present. 

1. Nonsense rhymes, such as Mother Goose. Rea- 
sons in favor — play in education, pleasure, interest; 
against — content lacking. 

2. Literature of familiar things, such as toys, games, 
food, domestic animals. 

3. Stories of primitive life of the race, early civiliza- 
tion, animal life, concrete heroism, Homer, Indian life, 
etc. Apply culture epoch theory. 

4. Fairy stories. Imagination sees the good and the 
beautiful. Should stories be condemned because the 
true is lacking? No. 

5. Fables. Literary inheritance. 

6. Myths. The story in education. 

7. Bible stories. 

8. Poetry. 



282 METHODS IN EDUCATION 

558. Principles determining the selection of reading 
matter. — The twofold relations of the individual and 
the community are factors for constant consideration. 
The mental requirements of the individual must be 
satisfied; the sociological or community interests must 
not be neglected. Hence, the two determining principles 
in the selection of reading matter are the psychological 
and the sociological needs. Such needs require 

1. Material simple in thought and form. 

2. Familiar words. 

3. Suitable content. 

4. Adaptability to individuals. 

Analytic Methods 

559. Analytic methods of teaching primary reading: 
word, sentence. — The word method in reading teaches a 
large number of words as wholes by associating the words 
with familiar things. The words are recognized at sight 
without knowing the speUing. Pupils have ideas when 
they enter school; they know many objects; they use 
many words; and so this method aims to teach pupils to 
recognize the words which are used in familiar language. 

560. Word method. — The advantages claimed for 
this analytic method are the following: 

1. The word is mastered by the eye. 

2. It is from the known to the related unknown, as 
children can talk words when they enter school, and now 
they learn that the word is a picture and also a sign of 
some objective thing. 

3. Alphabet, spelling, and syllables are learned in- 
cidentally. 

4. It is natural because languages are developed one 
word at a time, the word being the unit of language. 



READING 283 

Disadvantages of the word method: 

1. Mastery by the eye alone is not a pedagogical 
advantage; multiple sense instruction is better. 

2. Habit of guessing. 

3. Incomplete without phonics, spelling, and writing 
sentences. 

4. Considering the sentence as the unit of expression, 
the word method violates the principle from the whole 
to its parts. 

561. Sentence method. — This analytic method begins 
with sentences and works down to words and letters. 
Two advantages are claimed: 

1. The sentence is the unit of our language, since 
every complete thought must have a sentence for its 
expression. 

2. Interest, apperception, and self-activity used in 
constructing and interpreting sentences. 

Disadvantages of the sentence method: 

1. Incomplete without the study of words, letters, 
and phonics. 

2. Not suited to simultaneous teaching where dull 
pupils are present. 

Synthetic Methods 

562. Meaning. — The accepted meaning is given in 
section 210. Compare also sections 209, 211, and 212. 

563. Alphabet method. — The alphabet method 
teaches the letters first. Sooner or later the letters must 
be learned as they are instruments of knowledge in 
the child's mental equipment. It is, then, an advan- 
tage to learn them as soon as possible. But usage 
does not favor this method because (a) it violates 
the principle of going from wholes to parts; (6) it is 



284 METHODS IN EDUCATION 

neither the interesting nor the natural way of learning 
a language. 

564. Phonic method. — The learning of the sounds 
of the letters is not approved as the first step in learning 
to read. These are the reasons for disapproval: 

1. Some letters have too many sounds. 

2. Some letters are silent. 

3. The two arguments against the alphabet method. 

565. Advantages of phonic training. 

1. Pure tone. 

2. Distinct articulation. 

3. Power to read new words and pronounce them 
correctb^ 

Analytic-Synthetic Methods 

566. Distinction not accepted. — The two classifica- 
tions, analytic method and synthetic method,, are not 
accepted as distinct methods by all educators. We have 
already directed attention to the point that there can 
be no complete mental act without both analysis and 
synthesis; and, under this interpretation, we may reject 
any method that claims to be strictly analytic or syn- 
thetic alone, or we may show that the classification is 
defective. The latter is preferred. 

In the Psychology of Number, by McLellan and Dewey, 
we found an exposition of the mental process in passing 
from a vague whole to the definite. A similar psycho- 
logical process is fully explained in McLellan's Applied 
Psychology. If every child's mind passes through that 
process, then every method of teaching primary reading 
is analytic, even though the distinctive steps are syn- 
thetic. Hence, any of the approved methods discussed 
in this chapter may be called analytic-synthetic. 



READING 285 

567. Combination methods. — A liberal view of 
teaching primary reading includes the best features of 
the four methods mentioned. Thus the methods are 
made analytic-synthetic. Then add writing to co- 
ordinate motor activity; and, as another form of motor 
reaction, use dramatic expression as a means of interpre- 
tation through the aid of action. 

568. Dramatization. — The value of dramatic ex- 
pression is a modern contribution to primary reading. 
It need not be limited to primary reading, however, 
nor should it be. We have frequently emphasized the 
worth of oral expression in recitations, declamations, 
discussions, and debates. Here we add one more sug- 
gestion in regard to using the dramatic instinct of chil- 
dren in all grades as a means of individual and social 
interpretation, expression, and impression. 

In the N. E. A. Report for 1907, page 485, there is a 
short article on Dramatizing by T. C. Blaisdell, Professor 
of English Literature, State College, Lansing, Michigan. 
We quote three paragraphs and some of his suggestions : 

'' But why should not dramatizing be a potent factor 
in education? Children have an imagination far more 
vivid than have youths or adults. Left to themselves, 
unhampered by teachers and curriculum, children un- 
consciously become actors of power and dramatists of 
real human interest. 

To illustrate: A few days ago I attended the out-of- 
door flag-day celebration of a two-room rural school. 
The program had been left to a committee of five girls. 
They had of course the conventional recitations and 
songs, a violin solo, choruses, etc. 

But finally came an announcement that caused an 
expectant rustle among the fifty or sixty children and 



286 METHODS IN EDUCATION 

the few visitors sitting on the sloping hillside. Charades 
were announced, and we were to '' guess." They were 
not charades, however; they were effective Httle dramas, 
conceived entirely by the girls, without rehearsals, and, 
so far as I could learn, without any schoolroom experience 
in dramatizing. The Betsy Ross home during the mak- 
ing of the first flag was shown, the conversation between 
General Washington and his aides, and the famous flag 
maker, being given with a vividness that caused silence 
even among the boys of the somewhat restless audience. 
But the chief work of art was yet to come. Our young 
friend Malcolm was seen mounting his pony. He and 
his pony are a unit. And when he came crashing through 
the trees and in front of the audience crying " The 
British are coming! Be ready! Be ready! " he brought 
his audience to their feet. They cried out in their excite- 
ment, *' Paul Revere! Paul Revere! " The dramatizing 
was done with vigor, and was received with a dehght that 
does not pass. Will not Malcolm read of the famous ride 
of Paul Revere with a new power when next that poem is 
called for in the reading-class? And will not every boy 
and girl who saw the little play have a deeper under- 
standing of the real meaning of the original ride and read 
of it with added joy and with more dramatic skill? " 
569. Arguments for dramatization. 

1. Children are eager to interpret hfe; hence, the 
desire to play stories, poems, songs, and home or vaca- 
tion incidents. 

2. Visualization. Pupils comprehend better after 
seeing; they become better readers and better appre- 
ciators of literature. 

3. Overcomes self-consciousness. The enthusiasm is 
a powerful social stimulus. 



READING 287 

4. Clearer images formed. Better talking and writ- 
ing. 

5. Strengthens the speaking voice, gives ease of 
bodily carriage, increases desire for knowledge, brings 
teacher and pupils into closer relations, and exalts the 
function of pleasure as a factor in education. 

6. For reference, see Sara Cone Bryant's How to 
Tell Stories to Children; also, the books cited in 570. 

McCloskey Method 

570. Features. — This method of teaching reading 
combines the advantages of the four methods discussed 
in the preceding sections and also correlates reading and 
language. Special emphasis is placed upon the content 
of the reading matter. Some of the leading features are 
summarized : 

1. The choice of matter that appeals directly to the 
interests of the pupils. Live objects are selected, such 
as, the story of The Kid, from the Jewish Talmud; The 
Ox; The Little Red Hen; The Little Pine Tree; The Little 
Boy Blue. 

2. The vivid telling of stories by the teacher. The 
oral treatment of the story is the first step in the 
teaching. The story is told three times: first, to 
give an idea of the whole; second, to give the children 
a chance to fix the essentials in their right order; 
third, a rapid telhng to bring all the parts together 
again. For suggestions for oral work with stories, 
see DeGarmo's Essentials of Method, pages 94-107; 
McMurry's Method of the Recitation, pages 26-29; 
McMurry's Special Methods in Primary Reading, 
pages 1-46. 



288 METHODS IN EDUCATION 

3. The use of script forms in introducing the thought 
expressed in a sentence. Tliis process combines the 
sentence method and the word method. 

4. The transition from script to print. This puts 
the child into the use of text-book or printed sheets 
early in his school career. It gives him a chance to 
begin to help himself. 

5. Oral language lessons based upon the written and 
printed sentences already treated. A reproduction of 
the material already covered gives the teacher an 
opportunity to make use of the dramatic instinct in the 
children. This dramatic rendering of the little stories 
is not strictly a part of the McCloskey method but it 
is used successfully by a large number of teachers who 
are using the other points of advantage in the McCloskey 
method. The written language work follows closely after 
the first oral language work, and absolute accuracy in 
getting capitalization and punctuation is required from 
every pupil. The progress in the line of structural 
composition is one of the marvellous results of this 
method of teaching. 

6. Introduction of phonic lessons. After fifty or 
sixty words are thoroughly known at sight, the pupils 
are able to grasp the words as wholes and then the work 
in phonic analysis is introduced. The method of 
phonograms and blending is used. 

7. The letters of the alphabet learned and used. 
This summary of features shows that the McCloskey 
method does use the sentence method, the word method, 
the phonic method, and the alphabet method, but they 
are used in the reverse order from that advocated in 
some schools. The principle from the whole to the parts 
is rigidly observed in this method. 



READING . 289 



Ward Method 

571. Self-help. — This method is a combination of 
the word method and the phonic method. Later the 
other two methods are utihzed in the reading lesson. 
The aim of the Ward method of teaching reading is to 
make the child independent. The phonic drill during 
the first two years of the work aims to give the child a 
key to the language so that he will be able to help him- 
self in all the work in reading after the second and third 
years. 

572. Sight reading and drill. — The oral work in the 
Ward method is divided into three distinct lines of drill : 

1. Sight reading from the blackboard. 

2. Drill on phonograms. 

3. Drill on blend. 

In the first half year of school the children are taught 
to read eighty-two words by sight reading and in every 
instance the teacher must see that the children under- 
stand what they are reading. In teaching a word the 
actual process of teaching is not done until after the 
children have been tested to see that they have the gen- 
eral thought conveyed by that word. These words are 
used in sentences from the very beginning and are fre- 
quently drilled upon in conversation or story. Along 
with this sight reading there is much drill upon phono- 
grams and the blend. 

573. Features. 

1. The presentation of phonograms in a rational 
order. A phonogram is a written or printed representa- 
tion of a sound; as, f, 1, m, n, r, ing, ings, ight, ights. A 
word phonogram is a sight word used as a phonogram; 
as, ail, at, old. 



290 METHODS IN EDUCATION 

2. The teaching of an initial stock of phonograms 
before any phonetic reading is done. 

3. Thorough training in phonetic blending before 
any reading is done. This training aims to prepare the 
sense of hearing for quick, accurate perception. 

4. Gradual introduction of phonetic words into the 
sentences used in the reading lessons. A sight word is 
a word that has been taught as a" whole. Such words 
are recognized by the sight alone. A phonetic word is 
a word that the children are to read by means of com- 
bining the phonograms. The blend or blending is the 
union of simple or combined sounds into words. 

Aldine Method 

574. A general outline. — The actual procedure in 
the Aldine method is indicated by this outline: 

I. Preparation. 

1. Telling of the story. 

2. Dramatization of the story. 

II. Actual Reading. 

1. Writing of the rhyme on the board. 

2. Picture study. 

3. Repetition of whole rhyme by individuals while 
pointing to the several words. 

4. Instant recognition of the rhyme words pointed 
to promiscuously by the teacher. 

5. Recognition of rhyme words written promiscu- 
ously on the board. 

6. Drill with sight word cards. 

7. Drill on sentences from the chart. 

8. Seat work from the rhymes. 

III. Phonetics. 

1. Initial consonants (no diacritical marks). 



READING 291 

2. Vowel combinations and type words used with 
initial consonants to form word families. 

575. The method justified. — We have secured a 
brief exposition of Aldine Reading from one of the 
originators of that plan: 

* 'Aldine Reading as a plan or method is based on the 
natural interests, the spontaneous activities, the re- 
sponsive and creative imagination, the feelings and the 
knowledge of children living the active, happy life of 
childhood. Into this life Aldine Reading comes not as a 
task that is artificial, foreign, and distasteful — a drudgery 
to which children must submit because they are little; 
into the child's life Aldine Reading comes as a delight, 
as a most fruitful resource, offering varied and undreamed- 
of opportunities for joyful childish activity, growth and 
happiness. Hence the not uncommon occurrence of 
a child's suddenly discovering in surprise that he has 
learned how to read, that he can read, that he is reading, 
and that he likes to read! He had never realized that 
he was learning that difficult art. 

'^ But there is no magic about Aldine Reading. Like 
the marvellous achievements of applied science, its 
success depends upon the simple principle of understand- 
ing and utilizing, instead of ignoring and antagonizing 
nature. The child's nature furnishes the key, the sure 
guide to all the method there is in Aldine Reading. 
What does the child like — to see, to hear, to do? Does 
he hke stories, rhymes, pictures, ' make-believe ' 
games? All these he gets and takes part in from the 
very beginning. What subject, what content, must 
these stories, pictures, plays, and games have? Must 
they be full of simple action, full of appeal to the imagi- 
nation, with now and then a touch of mystery and won- 



292 METHODS IN EDUCATION 

der? Must the actors be animals and children and simple 
folk, fairies and personified objects of nature, with a 
strong bond of sympathy running through, uniting all 
and making them natural associates and playmates? 
All these simple requirements of childhood are satisfied 
in Aldine Reading. 

''The three fundamental elements of the power to 
read well are (1) a reading vocabulary composed at 
first of words and expressions already in familiar use in 
the spoken vocabulary; (2) the habit of instantly asso- 
ciating suitable thought and feeling with printed symbols 
and, in oral reading, of expressing naturally and effec- 
tively those thoughts and feelings; and (3) the power 
and the habit of mastering new language and thought 
independently. These three are developed constantly 
from the child's first day in school. Every exercise of 
every description contributes to this end, some exercises 
developing chiefly one, some another of these elements. 

'' Here we may barely indicate a few of the most 
important means employed to develop the three elements 
of power essential to good reading, as given above. Al- 
though all these elements are developed at the same 
time, in the beginning they are emphasized in the order 
named; as factors in making good readers, however, 
their relative importance would place them in the reverse 
order. 

''The initial reading vocabulary is acquired through 
the rhyme, the story, pictures, objects, and dramatizing; 
these, as means to the acquisition of a vocabulary, are 
of importance in the order named. The habit of 
associating suitable thought and feeling with printed 
symbols and, in oral reading, of expressing naturally 
and effectively those thoughts and feelings, is formed 



READING 293 

and fixed through dramatizing, the story, pictures, the 
rhyme, and conversation; these serve this purpose in 
about the order given. Just how all these objects and 
exercises are correlated and made to serve effectively in 
the development of the first two elements on which good 
reading depends, is explained in the Teacher's Manual: 

" The service of the exercises centring about these 
objects and ideas is not limited to the development of 
the first two elements of good reading; they also con- 
tribute to the development of the third and, in its far- 
reaching effect, the most fundamentally important of 
the three factors that determine good reading, the power 
and the habit of mastering new language and thought 
independently. In the development of this third factor, 
however, particularly so far as it has reference to the 
independent mastery by the child of the pronunciation 
and the thought of new words, most reliance is placed 
upon the treatment of phonics. Space permits here 
only the statement that children do learn in an in- 
credibly short time to read independently and fluently 
anything that is within the range of their understanding. 
And they can read what they are capable of understand- 
ing wherever it occurs, in books, papers, magazines, and 
manuscripts; they are not limited at any time to specially 
prepared books; diacritical marks — that abomination 
of children's readers — have no place in the Aldine. 
For the full explanation of the treatment of phonics 
reference must be made to the Manual. 

" The most fundamental principle in Aldine Reading 
is that the child shall apply from the beginning and con- 
stantly the knowledge that he has; that the teacher shall 
never do for the child what he can do for himself; and 
that all help given shall help the child to help himself. 



294 METHODS IN EDUCATION 

This one principle of independence, variously stated from 
various standpoints, pervades every exercise, whether 
it be reading, phonic drill, dramatizing, or picture study; 
it pervades equally all the variety of interesting and pur- 
posive seat work which contributes materially to the 
development of good reading. Aldine Reading is vastly 
more important than any mere method or device for 
acquiring mastery of the mechanics of reading — it 
does lead to that mastery speedily; it is all-round, rich, 
sound education for the primary child; and withal, it 
is a joy to child and teacher, as all primary education 
ought to be." 

576. Summary of advantages claimed 

1. Analytic system. 

2. Increasing interest stimulated. 

3. Self-rehance promoted. 

4. Abundant drill furnished. 

5. Power of expression stimulated. 

6. Self-activity always utilized. 

7. Visualization constantly used. 

8. Aesthetic appreciation developed. 

9. Associative laws followed. 

10. Systematic arrangement. 

11. Enables pupil to read alone from books at home 
within the first ten weeks of the school year. 

McCloskey and Aldine Combined 

577. Eclectic tendency. — A choice of what seemed 
best in the McCloskey and the Aldine methods has given 
us a combination method as applied in a Brooklyn school. 
This method has not been tested above the third grade, 
but still it is a type worthy of consideration. The 
McCloskey reading was abandoned in this grade 



READING 295 

because, at the start, it was found that the length of the 
sentences was too much for the beginners. 

The chart with its pictures, the stories suggested in 
the manual, the phonetic and sight word cards of the 
Aldine System aid the teacher in presenting the subject 
and help to hold the pupil's attention. Since this sys- 
tem is based upon a series of rhymes, it works nicely 
into the McCloskey System. The Aldine Manual is 
adhered to for directions, and each lesson is conducted 
along the following lines: 

1. Story is told by the teacher with the aid of the 
picture on the chart. 

2. Dramatization by the children in which the rhyme 
to be learned is repeated as often as possible. 

3. Rhyme is written on the board and drilled upon so 
as to associate the written form with the spoken word. 

The first rhyme consists of four different words. The 
second one has six new words. These ten words form 
a basis for numerous drill sentences in which the rhyme 
is eliminated. 

The sight word cards are used for the drills in recog- 
nizing the words already taught. These cards seem 
particularly good because the script form is on one side 
and the printed form on the other. 

When the children have mastered about six stories 
and are able to recognize readily the written form of 
the rhymes, print is introduced. The rhymes being 
known by heart, the printed form is easily learned. At 
this point the primer is started. For a certain number 
of pages the work is identical with that on the chart. 
The print being smaller, the pictures colored and the 
book itself something new, interest is still maintained. 

Phonetics are a part of the work, consonant sounds 



296 METHODS IN EDUCATION 

only being employed in the first grade. The phonetic 
cards also are well planned, one side containing the 
capital and the small form of a letter and the other side 
the small form and a word beginning with that particu- 
lar letter. 

578. Good reading defined. — Interpretation of the 
author is good reading. The analysis of this definition 
will show that it covers all of the mental and the physical 
quahfications of good reading. The physical qualities 
are articulation, enunciation, pronunciation, pitch, 
modulation, time, accent, and inflection. The general 
position of the body and the holding of the book con- 
tribute much to these quahties. The mental quahties 
are the results of an application of the physical qualities 
so that the selection may be properly expressed. This 
interpretation expressed involves emphasis, placing of 
rhetorical pauses, fluency, and feeling. 

579. Physical difficulties. 

1. Distinct articulation and enunciation. Appeal to 
imitative faculty of child, the teacher being the model; 
have individual and class drills on difficult sounds and 
combinations hke th in with, t in first, r in frog, k in 
sink. 

2. Modulation of voice. Work for pure speaking 
tones, the teacher being the model again. 

3. Weak attention. Have short, interesting lessons, 
and stop before interest wanes. Physical conditions 
often determine the duration of sustained interest. 
Timidity, bashfulness, and laziness should also be 
considered as causes. 

580. Mental difficulties. 

1. Association. Reading calls for a threefold effort: 
the idea in the mind, the spoken words, and the symbols 



READING 297 

representing these words. This association requires 
time, as required by DeGarmo's Law of Successive 
Clearness. 

2. InteUigence. Strive to get intelhgent reading, 
not a mere pronunciation of words. See the term 
appreciative reading in section 586. 

581. Reading to pupils. — In the lower grades the 
teacher's aim is to serve as a model in interpretation 
and expression, and, consequently, to arouse an interest 
in reading. The instinctive response through imitation 
is very strong. Aside from this desired reaction, the 
educative effect is powerful because the teacher's reading 
brings the content within the comprehension of the 
children. As the pupils advance in the grades the 
teacher's reading to them is not for the purpose of direct 
imitation by the pupil, but to increase interest and 
maintain a standard of good reading. 

582. Meaning of words. — The meaning of words 
should be learned through the context rather than from 
formal definitions. For various ways of teaching the 
meaning, see sections 289 to 295 inclusive. 

How to Arouse Interest in Reading 

583. Information and drill. — The substance of this 
section is in harmony with what was said about prepara- 
tion as one of the formal steps. See section 223. It has 
been suggested that, beginning in the second grade, 
'' The reading lessons proper should be preceded by (1) 
such conversations as may be necessary to prepare the 
minds of the pupils for the appreciation of the subject- 
matter, and (2) exercise which will insure the prompt 
recognition of the form and the meaning of new words." 



298 METHODS IN EDUCATION 

This second suggestion emphasizes the importance of 
drill as a means of reviving and clarifying old concepts 
to make them ready to blend with the new. 

584. Removing difficulties. — This process is a con- 
tinuation of the work in the last section, but the responsi- 
bility of finding and removing the difficulties must be 
shifted from the teacher to the pupils as soon as the 
pupils are capable of doing the work. In the fourth 
grade, for instance, pupils should use the diacritical 
marks as aids in the pronunciation of difficult words, 
and in the intelligent use of the dictionary. In all of 
this work, guidance is the function of the teacher, and 
consciousness of increasing power to help himself is 
the desired state of mind of the pupil. 

Every selection in reading has certain difficulties, 
and it is imperative that pupils acquire an effectual 
habit of removing the difficulties that are obstacles to 
good reading. But here we meet a pedagogical question: 
Does good reading require the removal of all difficulties? 
If so, is not practice in reading sacrificed to collateral 
research? We may leave this question unanswered 
and direct our attention to the following difficulties and 
remedies : 

1. New or difficult words. For a general treatment 
of teaching the meaning of words, see sections 289 to 295 
inclusive. 

2. Allusions and figures of speech. The teacher 
must be prepared in advance to explain whatever the 
child cannot find for himself. For allusions, give refer- 

. ence to pupils, if possible, and encourage them to look 
up the answers. 

3. Words, phrases, or clauses out of the natural order. 
The first treatment of this difficulty of order in a sentence 



READING 299 

is to lead pupils to arrange words, phrases, or clauses in 
the natural order, or the order commonly used in speak- 
ing. Then see why inverted or peculiar order is used in 
the selection. Is it for emphasis or climax? 

4. Ellipses, especially of verbs. Use suggestion just 
made, namely, look for the usual form of expression. 
Try to discover the contrast between the elHptical ex- 
pression and the full expression. What is gained by 
ellipses? 

5. Words used under poetic license in advanced gram- 
mar grades. Teacher must explain and then have 
pupils notice such uses thereafter. 

585. Enlarging native interests. — In the interme- 
diate grades, teachers should give informal talks on 
books to read at home, being guided in recommendations 
by tastes and interests of the individual pupils. This 
suggested reading may develop an acquired interest 
that will lead to usefulness and culture. Teachers have 
frequently reclaimed wayward children by tactfully 
recommending a book that satisfied youthful interest, 
even though the book was not in the prescribed reading 
for the grade. After an initial effort of this kind, the 
assignments can gradually make a transition to the 
literature of the grade. Judicious assignment means 
what all good teaching means, — an adaptation to the 
needs of the pupils. 

586. Appreciative reading. — In the first part of 
this chapter we spoke about the modern use of complete 
works in place of abstracts. It is the privilege of pupils 
to become familiar with all of Snow-Bound, Evangeline, 
Deserted Village, The Bunker Hill Oration, and other 
masterpieces that thrill the youthful mind by a realistic 
conception of human fellowship and literary power. 



300 METHODS IN EDUCATION 

One reading is not likely to arouse a lasting interest; 
and so three readings are advised, each having a specific 
yet related purpose. Have one rapid reading to get 
conception of the piece of literature as a whole; part of the 
reading may be done by teacher, part by pupils in class, 
and part by the pupils at home. A second reading should 
clear away the difficulties in meanings, and pupils should 
try to get the thought and feehng rather than the form 
of the selection. The third reading is for effective oral 
rendering of those parts of the selection which make special 
appeals to the pupils' imaginations and sympathies. 
I^v The three readings constituted what was formerly 
called critical reading of masterpieces. Now we call it 
appreciative reading, or interpretative reading, because 
the practice of critical study has produced another step 
in intellectual advancement. 

587. Oral reports. — The practice of giving occasional 
reports of collateral reading or other special assignment 
has the value already attributed to oral discussions and 
debates. Expression is a correlative of impression. 

588. Memorizing. — The recitation of selected por- 
tions of masterpieces need not be associated with drudg- 
ery and timidity. The boy who voluntarily commits to 
memory one hundred lines of the Deserted Village will 
not have to be told that Goldsm.ith's theme was close 
to the life of the people. Teach pupils how to memorize 
a selection, give them frequent practice in facing the 
class, and then one phase of interest in reading will be 
maintained by the pupils themselves. 

589. Silent reading. — A large part of the work of 
school and of life depends upon the power of reading 
silently. As all good reading means an interpretation 
of thought, it follows that the teacher's duty is to show 



READING 301 

pupils how to get the thought from the printed page 
through the process of silent reading. This may naturally 
follow the ability to do good work in oral reading, but 
special exercises to test the children upon the work in 
the reading lesson and in the library books are recom- 
mended. 

Articulati07i 

590. Violations of articulation. — Articulation has 
reference to the distinct utterance of the sounds of the 
letters and syllables constituting a word. This distinct 
enunciation is violated in four different ways. 

1. Suppression of a syllable; as, ev'ry for every, 
reg'lar for regular, and mem'ry for memory. 

2. The omission of sounds; as, readin for reading, 
swif'ly for swiftly, and Feb'uary for February. 

3. The substitution of sounds; as, ufford for afford, 
judgmunt for judgment, modist for modest. 

4. Blending of the termination of one word with the 
beginning of another; as, this sworld for this world. 

Accent and Emphasis 

591. Definitions. — Accent is the stress of voice 
placed upon a syllable; emphasis is the stress of voice 
placed upon one or more words in a sentence. The 
difference in accent is illustrated by the pronunciation 
of words, thus: conduct, meaning behavior, is accented 
on the first syllable; conduct, to lead, is accented on 
the second syllable. 

592. Emphasis illustrated. — Emphasis is frequently 
denoted in books by the use of italics, small capitals, or 
large capitals. But these indications are not always 
used, and so the interpretation of the piece to be read 



302 METHODS IN EDUCATION 

requires the student to place the emphasis so that the 
meaning of the author will be properly expressed. We 
give two illustrations from the Union Fifth Reader, by 
Sanders : 

'' Liberty and Union, Now and Forever, One and 
Inseparable." 

Treason! cried the speaker; treason, treason, 
TREASON, re-echoed from every part of the house. 

Absolute emphasis is the kind just illustrated. It 
belongs to the important words in a sentence, irrespec- 
tive of contrasting emphasis. Antithetic emphasis 
depends upon contrasting parts of a sentence. 

" People do not lack strength; they lack will.'^ 

Inflection 

593. Meaning and kinds. — The word inflection 
means a rising or a falhng of the voice in reading or 
speaking. The four kinds of tones classified under 
inflection are the monotone, the rising inflection, the 
falling inflection, and the circumflex. Strictly speaking, 
the monotone is not an inflection at all because there is 
no rising or falling, but for convenience it is classified 
with the other three kinds of tones. Following is an 
illustration for each kind of tone. 

594. Monotone. 

^' Thy will be done." 

595. Rising inflection. 

The noisy geese that gabbled o'er the pool, 
The playful children just let loose from school; 
The watch-dog's voice that bayed the whispering wind, 
And the loud laugh that spoke the vacant mind; 
These all in sweet confusion sought the shade. 
And filled each pause the nightingale had made. 



READING 303 

In these lines from the Deserted Village, use rising 
inflection on pool, school, wind; falling on shade and 
made. 

596. Falling inflection. 

Brutus. Go to; you are not, Cassius. 

Cassias. I am. 

Brutus. I say you are not. 

Cassius. Urge me no more; I shall forget myself. 

Have mind upon your health; tempt me no further. 
— ^From Jidius Caesar. 

Falling inflection on to, not, Cassius, am, not, more, 
myself, health, further. 

597. Circumflex for underscored words. 

And this man has become a god, and Cassius a wretched 
creature. 

Modulation 

598. Kinds : pitch, quantity, quality. — Modulation 
has reference to the variations in the voice in speaking 
and reading. Modulation is both mental and physical 
and it depends upon the emotional interpretation of the 
selection to be read. 

Modulation is expressed in three different ways. 
Pitch has reference to high or low tones of the voice; 
quantity means the volume or the loudness of the tones; 
quality has reference to the kind of tone. Pitch is 
easily distinguished by associating it with the musical 
scale. Quantity is measured by the volume of the sound, 
as soft or loud; and by the time, as slow or quick. Volume 
has reference to the stress; time has reference to the 
movement. Illustrations of the principal characteristics 
under quantity are given below. Number (1) is high 
and loud; (2) very loud; (3) quick; (4) soft; (5) very 



304 METHODS IN EDUCATION 

loud; (6) plaintive; (7) and (8) slow and low. Selection 
and application taken from page 44, Union Fourth 
Reader, by Sanders. 

(1) The combat deepens ! (2) on ! ye brave ! 

(3) Who rush to glory, (4) or the grave! 

(5) Wave, Munich! all thy banners wave! 
And charge with all thy chivalry! 

(6) Ah! few shall part where many meet! 
The snow shall be their winding sheet, 
And every turf beneath their feet 

(7) (8) Shall be a soldier's sepulchre! 

— Campbell. 

Quality of Tone 

599. Meaning. — Quality relates to the kind of tone. 
Under ordinary classifications there are the four kinds. 
Sanders, an authority followed by nearly all the modern 
books, gives four definitions which we shall quote: 

600. Pure tone. — The pure tone is a clear, smooth, 
sonorous flow of sound, usually accompanied with the 
middle pitch of voice, and is adapted to express emotion 
of joy, cheerfulness, love, and tranquillity. 

Example 

Hail! beauteous stranger of the wood, 

Attendant on the spring, 
Now heaven repairs thy vernal seat. 

And woods thy welcome sing. 

601. Orotund. — The orotund is a full, deep, round, 
and pure tone of voice, peculiarly adapted in expressing 
sublime and pathetic emotions. 



READING 305 

Example 

It thunders! Sons of dust, in reverence bow! 

Ancient of Days! Thou speakest from above: 

Almighty! trembhng, hke a timid child, 

I hear thy awful voice. Alarmed — afraid — 

I see the flashes of thy lightning wild, 

And in the very grave would hide my head. 

-602. Aspirated tone. — The aspirated tone of voice 
is not a pure, vocal sound, but rather a forcible breathing 
utterance, and is used to express amazement, fear, 
terror, anger, revenge, remorse, and fervent emotions. 

Example 

Oh, coward conscience how dost thou affright me! 
The lights burn blue. It is now dead midnight; 
Cold, fearful drops stand on my trembling flesh. 

603. Guttural quality. — The guttural quality is a 
deep, aspirated tone of voice, used to express aversion 
hatred, loathing, and contempt. 

Example 

Tell me I hate the bowl? 

Hate is a feeble word: 
I loathe, ABHOR, my very soul 

With strong disgust is stirred. 
Whene'er I see, or hear, or tell, 
Of the dark beverage of hell. 

Pauses 

604. Grammatical and rhetorical. — Rhetorical pauses 
are those made in reading, irrespective of the construe- 



306 METHODS IN EDUCATION 

tion or the punctuation of the passage. Grammatical 
pauses are those made in accordance with the construc- 
tion and the punctuation of the passage. The former 
is illustrated: 

Sweet was the sound | when oft at evening's close | 
Up yonder hill 1 the village murmur rose I 

605. Control of the breath. — As in all other school 
work there are two conditions to be considered, the 
physical and the mental. We have already spoken about 
the necessity of good physical conditions in each child 
and the consequent mental conditions. Good breathing 
requires proper position in sitting and standing. It 
involves practice in deep breathing and the general 
poise of mind and body. The child that is taught to 
breathe deeply will soon form the habit of breathing in 
that way most of the time. When he comes to the prac- 
tice in oral reading, the breathing will then take care of 
itself and his attention can be given to the mental 
qualities of good reading, while the breathing will supple- 
ment his interpretation by means of the oral expression. 
The ordinary ''setting up" exercises in physical culture 
are intended to put the body into physical conditions 
for effective breathing in all school work. 

606. Extensive and intensive reading. — Extensive 
reading refers to the amount of reading done by the 
pupil; while intensive reading relates to the depth of 
the interpretation made. The present tendency is 
toward extensive reading. Stanley Hall and some other 
educators advocate the mastery of one good book in 
literature rather than the promiscuous reading of books. 
The latter may seem to satisfy the desires and views of 
the child, but there will be a lack of classified material 



READING 307 

or an utter forgetfulness of the matter read. Intensive 
reading of a few good books will enable the pupil to get 
the thought of the author, to become familiar with the 
author's style of writing, and to form ideals worthy of 
imitation. There are arguments in favor of each kind 
of reading, but a personal opinion favors the latter kind. 

607. Home reading. — The class library is designed 
to supplement school work and to furnish the teacher 
with such material as will attract the children to books, 
create a love for good literature, and encourage the 
habit of reading outside of school hours. A good rule 
to be followed in the selection of books is the one laid 
down by Dr. Hill in The True Order of Studies: 
'' The most instructive reading for a person of any age, 
old or young, is that in which the author's tone of thought 
is above the average tone of the reader's thought, and 
yet not beyond his grasp." 

The pupils should have convenient access to the hbrary 
for reference work and general reading. They should 
be encouraged to draw books and take them home. 
Books should be kept not longer than two weeks without 
renewal; and such books as are in great demand 
should not be retained by a pupil more than one week. — 
New York Course of Study. 

608. Literature and character. — This topic is in- 
serted here to emphasize the need of more direction 
regarding what children shall read. The teacher of 
ordinary reading is supposed to give the child the power 
to interpret good literature, but her task does not end 
with that part of the work; she must supplement those 
efforts in teaching by trying to direct the child into 
habits of reading a kind of literature that will form 
character for life. 



308 METHODS IN EDUCATION 

609. Patriotic selections. — There are two views 
regarding the teaching of patriotism. One mentions 
specific virtues in civic life and then proceeds to teach 
the necessity of having these virtues. This teaching is 
done largely through biography and history. The 
tendency toward imitation of the lives of great men and 
women is the principle upon which this kind of training 
rests. The other view is through the self-activity of 
the pupils in organizations for pupil self-government 
and in the supplementary reading of chosen selections 
which convey the highest ideals in American life. The 
latter process is the one that justifies the use of patriotic 
material in the course for reading. Such material 
exalts civic virtues, which are treated abstractly in the 
first view of patriotic training, but the teacher does not 
preach the necessity of following every one of these 
virtues. She hopes, however, to have the pupil, through 
the interpretation of the literature, recognize the ideals 
and feel it a duty and a pleasure to strive to attain such 
standards. 

610. Biography. — In the chapter on history we 
spoke of biography as a correlated means of making 
historic events emphatic. A similar use may be found 
in reading. The selections in literature will have a 
stronger personal relation as the child becomes acquainted 
with the lives and characteristics of the author. This 
point of view alone justifies the use of a certain amount 
of biography as a part of the suitable material in the 
course in reading. 

How to Memorize a Selection 

611. The selection. — Choose a selection that will 
appeal to the interests of the class. It may be necessary 



READING 309 

to educate the children to appreciate certain kinds of 
prose or poetry. In this process of education teachers 
should select material that will suit the children during 
the various steps in their development. 

612. Copy in .sight. — Use a selection that may be 
found in the books of the class so that each child may 
have a copy for his own use. If this is not possible, 
write the whole selection on the board so that it may 
be easily seen from any part of the room. 

613. Biography of author. — Bring out the essential 
facts in the biography of the author. 

614. Occasion of writing. — Show the conditions 
which led to the writing of the selection. 

615. Business-like attack. — Don't make a long in- 
troduction in trying to arouse interest. Make the teach- 
ing of the selection a matter of business which every 
child in class ought to respect. The very fact that the 
selection has been chosen for this purpose is enough to 
invite respectful attention; and the facts brought out 
in the biography and in the conditions at the time of 
writing the selection are enough to interest an average 
class. 

616. Physical comfort. — Have the pupils take a 
comfortable position, fix attention upon the matter on 
the board, and prepare themselves for concert work. 

617. The memorizing. — The teacher should diriect 
the lesson by having all pupils read the whole selection 
through once. Then take it by stanzas or paragraphs, 
and then the third time begin upon the sentences. 
Concert memorizing of a certain amount of the selection 
is made by means of visualization. Concert drill and 
individual drill follow. 

618. Unifying review. — Review frequently from the 



310 METHODS IN EDUCATION 

beginning so that pupils may hold the parts in their 
relation to the whole. Do not prolong the work to the 
point of fatigue. Grade selection according to the abihty 
of the class to memorize, and stop when the complete 
selection is mastered. The completion of the process 
may be assigned for home work. 

619. Rhetorical exercises. — The practice of having 
rhetorical exercises, from time to time, is to be com- 
mended as a useful exercise in school work. Those 
who have read the substance of this book do not need 
an extensive answer to this question. Such exercises 
are a kind of oral summary of the leading points in all 
the lessons; but as a means of bringing out the dramatic 
element in expression they have a far greater value. 
From what has been said about class discussions, debates, 
etc., students can summarize the points of value in 
rhetorical exercises. 

620. Adaptation. — We have emphasized the necessity 
of adaptation all through the grades in the elementary 
schools and so that general principle can be applied to 
every exercise in the course in reading. 

621. Variety. — The law of variety is a physical and 
a mental necessity. It is the one valuable point in the 
avoidance of fatigue. As the reading matter is one 
external means of adapting variety, it is not necessary 
to offer a longer defence of its use. 

622. Correlation. — Since reading is necessary as a 
basis for all studies, it follows that reading must be 
correlated with all studies. It is not necessary, however, 
to make the recitation periods in reading lose their 
character as such in the effort to cover the work in 
geography, grammar, arithmetic, or other studies. 



READING 311 

Memory Gems 

623. Limitations. — To what extent should pupils 
be required to memorize gems from literature? What 
should be the characteristics of such memory selections? 

A minimum assignment should be prescribed for every 
grade in the elementary school. The selections are 
intended to aid pupils in thought and expression rather 
than to serve as mere training for the memory. Each 
sele'ction has the merit (a) of being adapted to the grade, 
(h) of teaching some desirable lesson, (c) of possessing 
literary excellence. 

New York City Suggestions 

lA 

At least four lines of poetry per week, or an equivalent 
amount of prose, should be memorized by every pupil. 
The selections may be made from the following list: 

Little Pussy — Taylor. The Dewdrop — Sherman. 
Who has Seen the Wind? — Rossetti. Sleep, Baby, 
Sleep (two stanzas) — From the German. The Rain 
is Raining All Around — Stevenson. The Wind — 
Stevenson. Boats Sail on the Rivers — Rossetti. 

Mother Goose Rhymes: Humpty Dumpty. Mistress 
Mary. Little Jack Horner. Little Bo-Peep. Little 
Boy Blue. Baa, Baa, Black Sheep. Rock-a-by, Baby, 
Thy Cradle is Green. Rock-a-by, Baby, on the Tree 
Top. .This Little Pig Went to Market, etc. 

iB 

The Sunbeams — Poulsson. Over in the Meadow — 
Wadsworth. Hush! the Waves are Rolling in — Old 



312 METHODS IN EDUCATION 

Gaelic Lullaby. What Does Little Birdie Say? — Ten- 
nyson. The Baby — MacDonald. The Golden Rule — ■ 
New England Primer. Robin Redbreast — AUingham. 
Twinkle, Twinkle, Little Star — Taylor. Nonsense 
Alphabet — Lear. 

Mother Goose Jingles: Sing a Song of Sixpence. I 
Saw a Ship a-SaiUng. I had a Little Sister. Peter 
Piper. As I Went Through the Garden Gap, etc. 
Thirty White Horses. Little Nancy Etticoat. The 
House That Jack Built. 

2a 

The Swing — Stevenson. Bed in Summer — Steven- 
son. Who Stole the Bird's Nest? — Child. Daisies — 
Sherman. Seven Times One — Ingelow. The Rock- 
a-By Lady — Field. All Things Beautiful — Alexander. 
Proverbs and Maxims. 

2b 

Don't Kill the Birds — Colesworthy. Ariel's Song, 
'' Where the bee sucks." — Shakspere. My Shadow — 
Stevenson. Dutch Lullaby — Field. Windy Nights 
— Stevenson. Lady Moon — Houghton. Stop, Stop, 
Pretty Water — Follen. The Land of Story Books — 
Stevenson. 'Thanksgiving Day — Child. Proverbs and 
Maxims. 

'3a 

I Live for Those Who Love Me — Anon. The Brown 
Thrush — Larcom. The Tree — Bjornsen. Wishing — 
AUingham. The Owl and the Pussy Cat — Lear. The 
Violet — Jane Taylor. Hiawatha's Childhood — Long- 
fellow. Hiawatha's SaiUng — Longfellow. Proverbs and 
Maxims. 



READING 313 



3b 



The Child's World — LiHiput Lectures. Marjorie's 
Almanac — Aldrich. A Visit from St. Nicholas — 
Moore. The Owl — Tennyson. The Captain's Daugh- 
ter — Field. Sweet and Low — Tennyson. Proverbs 
and Maxims. 

4a 

The Night Wind — Field. The Children's Hour — 
Longfellow. Jack Frost — Gould. Robert of Lincoln 

— Bryant. ''He Prayeth Best " — Coleridge. The 
Wreck of the Hesperus — Longfellow. 

4b 

The Fountain — Lowell. September — Jackson. The 
Village Blacksmith — Longfellow. The Mountain and 
the Squirrel — Emerson. Barefoot Boy — Whittier. 

Drill exercises, as in 4a. 

5a 

The Landing of the Pilgrims — Hemans. The Day 
Is Done — Longfellow. '' Under the Greenwood Tree " 

— Shakspere. A Sea Dirge — Shakspere. Woodman, 
Spare That Tree — Morris. The Gladness of Nature — ■ 
Bryant. Excelsior — Longfellow.. The Arrow and the 
Song — Longfellow. 

5b 

The World Wants Men — Anon. Aladdin — Lowell. 
Psalm of Life — Longfellow. To the Fringed Gentian — 
Bryant. The Planting of the Apple-Tree — Bryant. 
Paul Revere's Ride — Longfellow. Barbara Frietchie 

— Whittier. Today — Carlyle. 



314 METHODS IN EDUCATION 



6a 

Orpheus with His Lute — Shakspere. The Destruc- 
tion of Sennacherib — Byron. A Man's a Man for A' 
That — Burns. The Minstrel Boy — Moore. Abou 
Ben Adhem — Hunt. The First Snow-Fail — Lowell. 
Nobility — Gary. Sheridan's Ride — Read. Song of 
Marion's Men — Bryant. 

6b 

The Spacious Firmament — Addison. Burial of Sir 
John Moore — Wolfe. The Builders — Longfellow. Old 
Ironsides — Holmes. One by One — Proctor. '^ Breathes 
there the Man " — Scott. The Blue and the Gray — 
Finch. The White-Footed Deer — Bryant. 

7a 

Fiftieth Birthday of Agassiz — Longfellow. To a 
Waterfowl — Bryant. The Finding of the Lyre — 
Lowell. The Year's at the Spring — Browning. " It 
is not growing like a tree " — Jonson. Daybreak — 
Longfellow. Bannockburn — Burns. 

7b 

Thanatopsis — Bryant. Gharge of the Light Brigade 

— Tennyson. Hohenlinden — Gampbell. " Good name 

in man and woman " — Shakspere. " Farewell, along 

farewell to all my greatness " — Shakspere. The Bugle 

Song — Tennyson. " There was a sound of revelry " — 

Byron. 

8a 

" Thou, too, sail on " — Longfellow. '' The quahty 
of mercy '*' — Shakspere. The Ghambered Nautilus — 



READING 315 

Holmes. My Heart Leaps Up — Wordsworth. The 
Brook — Tennyson. Sound the Loud Timbrel — Moore 
'' I wandered lonely " — Wordsworth. The Concord 
Hymn — Emerson. Opportunity — Sill. Warren's Ad- 
dress — Pierpont. Bunker Hill Oration — Webster. Po- 
lonius's Advice — Shakspere. 

8b 

Liberty and Union — Webster. To a Skylark — 
Shdley. Elegy — Gray. The Forest Hymn — Bryant. 
Commemoration Ode (Division VI.) — Lowell. On 
His Bhndness — Milton. The Way to Heaven — Hol- 
land. Sandalphon — Longfellow. '' This was the noblest 
Roman of them all " — Shakspere. Gettysburg Ad- 
dress — Lincoln. '' What is so rare as a day in June " 
— Lowell. 



CHAPTER XV 
ARITHMETIC 

624. Changing points of view. — During the last ten 
years the teaching of mathematics has had more vigorous 
and authoritative discussion than any other subject in 
the elementary schools. The investigative efforts have 
produced a new psychology of number and new concep- 
tions of methods, reconstructed text-books representing 
new types in content and arrangement, and established 
public recognition of the pertinent value of the history of 
mathematics. When we consider that arithmetic was 
co-existent with the needs of man, it is surprising that 
evidence of systematic reconstruction is not found in the 
earlier epochs of intellectual activity. But regrets are 
needless since students are privileged to share the ben- 
efits of modern scholarship. For references, see list of 
books at the end of this chapter. 

625. Quantity, measurement, mathematics. — One 
notable feature of the new conception of mathematics is 
the close relation of arithmetic to life. This relation 
has always existed, but it has not been recognized in 
theory and application. The fundamental idea in each 
of the three topic headings in this section is found in 
the needs and hmitations of mankind. Our wants are 
many, but provision for their supply is limited and 
secured only by labor. Time and energy are limited. 
It comes about, consequently, that the question how 

316 



ARITHMETIC 317 

much enters largely into life. How much do I need? 
How much can I get? How much of my time shall I 
give to this portion of my task, and how much to that? 
How much is mine? How much is yours? These and 
a thousand other similar questions are very insistent. 
Success in life depends largely upon the wisdom and 
accuracy with which we answer them. 

A more specific illustration of this quantitative side 
of life is found in the historic experiences of the race. 
Take the pioneer farmer's problem, for instance. Land 
must be cleared and plowed and planted. The crop 
must be cultivated and harvested, a barn to store the 
grain and a shelter for family and stock must be built. 
Many other tasks must be performed. All these are 
essential parts of his one great task. Not one can be 
neglected, but almost any one might absorb all of his 
time and energy. He might build so large as to have 
no time for other things. He might clear so much land 
as to have no time left for plowing and so on. He 
must decide how much time he can give to any one part 
of his task and yet do justice to all the rest. In each 
separate task he must decide how much to undertake 
so that he may finish the task in its allotment of time. 
All thi^ is true under the primitive conditions; and as 
social organization develops, the question how much 
becomes far more insistent and frequent. 

Definitions 

That aspect or property of the outside world that 
presses upon us the question how much may be thought 
of as quantity. 

The process of determining the answer to the question 
how much is measurement. It is not always or gen- 



318 METHODS IN EDUCATION 

erally a simple process of laying off a unit. That is, 
of course, always involved, but the entire process gen- 
erally involves also considerable computation guided by 
knowledge of geometrical or physical laws. 

The science of quantity is mathematics; and, therefore, 
mathematics is the science that treats of measurement 
and all the geometric and physical laws that measure- 
ment involves, and the application of those laws in 
computation, as well as the art of computation itself. 

626. Definition of number. — The answer to the ques- 
tion of quantity, the result of the process of measure- 
ment, is number. This is identical with the definition 
found in many arithmetics: '' Number is that which 
answers the question how many or how much.'' The 
question how much always resolves itself into how many, 
according to Psychology of Number, page 71. Number 
is, then, that in which our ideas of quantity become 
definite. 

The following definition regards the origin as well as 
the use of number: Number is a product of the way 
in which the mind deals with objects in the operation 
of making a vague whole definite. — McLellan and 
Dewey, page 32. 

Note that this definition considers the concept of 

number as the result of a mental process showing 

quantity. 

Other Approved Definitions 

1. A number is that which is applied to a unit to 
express the comparative magnitude of a quantity of the 
same kind as the unit. — Glashan, Arithmetic for High 
Schools. 

2. Number is the abstract ratio of one quantity to 
another of the same kind. — Newton. 



ARITHMETIC 319 

3. Number is the ratio of one quantity to another 
quantity taken as a unit. — Euler. 

Disapproved Definitions 

1. ''Number is a symbol." Entirely abstract; wrong, 
not in the mind. 

2. "Number is identical with things; it is a property 
of objects." Wrong, as concept of number can exist 
only in the mind. It is because objects have been used 
to develop the idea of number that these definitions have 
been used. While we put number into objects, we 
derive our idea of number from the objects themselves. 

3. ''Number is a collection of units." Smith, page 
100, says this definition is " scientifically worthless." 
But some educators hold that the first number concept 
is a collection of units, the ratio idea not developing 
clearly until later. This definition as quoted does, of 
course, exclude one as a number. 

Conclusion 

The consensus of opinion favors the definitions making 
number identical with ratio. 

The definition quoted from McLellan and Dewey is 
generally accepted. Another authoritative source is 
Smith's The Teaching of Elementary Mathematics. The 
quotations used by Smith on pages 99, 100, and 101 
are serviceable here: 

The notion of number is not the result of immediate 
sense-perception, but the product of reflection, of an 
activity of our minds. We cannot see nine. We can 
see nine horses, nine feet, nine dollars, etc., that is, we 
see the horses, the feet, the dollars, if they are presented 
to us; that there are exactly nine, however, we cannot 



320 METHODS IN EDUCATION 

see. If we wish to know this we are forced to count the 
things; and since we usually do this with the help of 
our eyes, the idea has got abroad that we see number. 
— Fitzga, Die naturliche Methode des Rechen- Unter- 
richtes in der Volks- und BUrgerschule, I. Theil, Wien, 
1898. 

Number is generated in the mind by the seiSe-percep- 
tion of a group of things supposed to be alike. — Smith, 
page 101. 

A careful observation shows us, however, that there 
are no objects exactly alike; but by a mental operation 
of which we are quite unconscious, although it holds 
within itself the entire secret of mathematical abstrac- 
tion, we take in objects which seem to be alike, rejecting 
for the time being their differences. Here is to be 
found the source of calculation. — Laisant, La Mathe- 
matique, pages 15, 18, 19, 31. 

627. Counting and measuring. — There is much dis- 
cussion about whether counting or measuring should 
come first in teaching number. Both are required, but 
the New York City course of study mentions counting 
first. This use of the term counting includes the four 
fundamental operations; the old notion of counting 
meant a mastery of the numbers 1, 2, 3, 4, etc., in a 
narrower sense. Measuring is simply a form of activity, 
a kind of reaction. It implies learning by doing; it is 
concrete; it is empirical; it should be definite work 
rather than educative play. Measuring stimulates 
interest if the pupil understands what he is doing when 
he is measuring; but he cannot have any definite con- 
cept of measurement until he counts by using some unit 
of measurement, such as foot, yard, pint, dime, etc. 
Hence, ''all counting is measuring and all measuring is 



ARITHMETIC 321 

counting," as is said in McLellan and Dewey's Psychol- 
ogy of Number, page 48; also in Smith's The Teaching 
of Elementary Mathematics, page 104. When we count 
books in a hbrary, we measure the Ubrary; and we meas- 
ure our weight by counting the number of pounds. 
Counting is measuring a magnitude composed of dis- 
cernibly distinct units; measuring is a method of 
counting the units into which a magnitude, outwardly 
continuous, may conceivably be divided. 

*The difference between counting and measuring is 
that in ordinary counting we use an undefined unit, a 
kind of vague measurement; as, 10 apples, 5 books. 
This counting of 10 apples or 5 books becomes definite 
only when weight or value, i.e., measure, is known. The 
two processes help each other toward the same object, 
determination of quantity. 

628. Arithmetic and its aim. — Arithmetic is a Greek 
word meaning literally science of number, and that is 
its traditional definition. But the word is used by us 
to describe the mathematics of the elementary school 
course, which is necessarily much more and at the same 
time much less than the science of number. What we 
thus call arithmetic might more properly be called the 
elements of mathematics, since the elements of geometry 
and physics have as legitimate a place in it as number, 
although the number element is large as compared with 
other elements. The subject-matter of arithmetic must 
be mathematical operations, processes, principles; but the 
aim of arithmetic is not so much the mastery of those 
processes and principles, as their application to the 
problems of measurement in the world about us. That 
application means the mastery of our material surround- 
ings, familiarity with the quantitative side of nature, 



322 METHODS IN EDUCATION 

insight into the world we Hve in, and command over its 
resources. The authorities for this view are McMurry, 
page 19; Smith, Chapter II and page 89; Harris, in 
Educational Review, Vol. 9, page 231; Young, page 203, 
for statement of aim of teaching arithmetic. 

The obvious aim is to give accuracy and facility in 
simple computations and a working knowledge of prac- 
tical applications; but, as Young points out, the teacher 
who works for no other end will miss a thousand oppor- 
tunities to invigorate the pupil's power of thought. All 
the practical usefulness of arithmetic can be attained 
without sacrificing its value in cultivating habits of 
observation and reflection. 

The Scotch Education Department memorandum on 
Teaching Arithmetic in the first years states as the 
first aim of the teacher: The development of the pupils' 
interest and inteUigence through the solving of concrete 
problems with a clear understanding of the processes 
involved; and, as the second aim, the gradual perfecting 
of the machinery for the manipulation of abstract num- 
bers. It should be added that a definite aim is the most 
important thing connected with method. {Smith, pages 
1 and 110.) 

629. Utility of arithmetic. — It thus appears that 
''arithmetic is the indispensable first step toward all 
science of nature." ''Historically it was the first tool 
of thought that man invented in the work of emanci- 
pating himself from thraldom to external forces." "It 
is a powerful instrument for the regulation of social 
intercourse." The utihty of the subject of study that 
occupies this position is obvious, and nearly all nations 
have put special utilitarian value upon it. Smith points 
out that the utility of mathematics for the individual in 



ARITHMETIC 323 

helping him to earn a Hving has been overrated. That 
is in a measure true, but it is also true that, in a larger 
sense, the utility of mathematics as a means of correlat- 
ing the child with the world he is to live in cannot be 
overrated. For further discussion, see Educational 
Value of Mathematics, Frank A. Hill, Ed. Rev., Vol. 9, 
page 349; also W. T. Harris, Ed. Rev., Vol. 9, page 242. 

630. Important historical facts. — The Roman nota- 
tion was used in Europe during the classical times and 
up to the fifteenth century. That notation served 
clumsily and inadequately the purpose of recording 
number, but was of no use for assisting computation. 
For this latter purpose some form of the abacus, in 
which counters in different grooves represented units of 
the various decimal orders, was used. Thus, both the 
teaching of arithmetic and the method of computation 
were objective. 

About 1500 A.D., the Hindoo, commonly called the 
Arabic, system was adopted. This furnished an ideal 
means of assisting computation, and teachers, perceiving 
that their objective devices were no longer needed for 
computation, supposed that the devices could be dis- 
pensed with altogether. Arithmetic came to be a thing 
of symbols exclusively, and so also did the teaching of 
arithmetic. The teaching of arithmetic became the 
inculcating of a vast body of rules for juggling with 
digits. This was the age of rhyming arithmetics. It 
was hoped that if the rules were turned into rhyme the 
pupils would more easily remember them. 

Not until shortly before the beginning of the nine- 
teenth century was there a return to a more rational 
system. The great reformer was Pestalozzi. He reso- 
lutely made sense-perception the basis of all number 



324 METHODS IN EDUCATION 

work and' insisted that arithmetic should not be a 
matter of rules and traditions, but a rational process 
from beginning to end. His reforms were bitterly- 
assailed and opposed, and only partially adopted. The 
battle still goes on. Compare for example the radically 
different views of objective teaching in the early school 
years as given in the New York City Syllabus and the 
1910 State Syllabus. 

A brief summary of historical views shows that 
thinkers have been contributing point by point what 
some recent writers seem to consider entirely new. A 
grouping of these respective contributions gives the 
substance of modern ways of teaching. Consult Smith 
for full presentation. 

1. Busse. Number pictures: number cards of today. 

2. Pestalozzi. Observation = perception, 
(a) Know numbers rather than figures. 

(6) Objective presentation; remove objects before 
drill. 

(c) Much oral abstract drill. 

3. Tillich. Special blocks: ratio. See Speer method. 

4. Kranckes. Concentric circles. 10, 100, etc. 
Spiral methods. 

5. Grube, 1842. All processes simultaneous. 1 to 
10 first year. 

6. Tank and Knilling; counting, 
(a) Numbers needed for counting. 

(6) Use number series. 2468, etc.; count objects, 
then memorize. 

(c) Counting is basis of all elementary operations. 

7. German spiral method based on concentric circles. 

8. Arithmetic in rhyme. 

9. All arithmetic based upon measurement of lines. 



ARITHMETIC 325 

10. All arithmetic based upon paper folding. 

11. Rein. Correlation. 

(a) Familiar objects in home, nature study, literature, 
etc. 

(6) Series and method units. 

(c) Formal steps of instruction. 

631. Method in arithmetic. — It would be impossible 
to form one composite method from the various lines of 
thought in mathematics. There is no unified historic 
development. We must look to recent psychological 
conclusions, as stated in the first section of this chapter. 
Four opinions will help to strengthen the opinion on 
general method as expressed in Chapter VIII. 

1. There is no subject taught in the elementary 
schools that taxes the teacher's resources as to methods 
and devices to a greater extent than arithmetic. There 
is no subject taught that is more dangerous to the pupil 
in the way of deadening his mind and arresting its 
development if bad methods are used. — W . T. Harris 
in Editor's Preface to the Psychology of Number. 

2. ''Sound methods are methods that capture the 
interest, supply the will with motives, enlist the reason- 
ing powers, favor original thought, and put the student 
on his intellectual mettle." ''The methods need to be 
so graded as to give the student the consciousness of 
power." — F. A. Hill, Ed. Rev., Vol. 9, page 350. 

The problem of method is always the same : — to 
interest the pupil, to induce research, to continually 
give him the notion, the illusion if you will that he is 
discovering for himself the things that are being taught 
him. — M. Laisant, quoted by Smith, page 109. 

Enough has been said to show that one of the easiest 
things in the teaching of arithmetic is the creation of 



326 METHODS IN EDUCATION 

''Method" — and one of the most useless. We may 
start off upon the idea that all number is measure, and 
hence that arithmetic must consist of measuring every- 
thing in sight — and we have a ''Measuring Method." 
It will be a narrow idea; we shall neglect much that is 
important; but if we put energy back of it we shall 
attract attention and will very likely turn out better 
computers than a poor teacher will who is wise enough 
to have no "Method," in this narrow sense of the term. 
Again, we may say that every number is a fraction, the 
numerator being an integral multiple of the denominator 
in the case of whole numbers. From this assumption 
we may proceed to teach arithmetic only as the science 
of fractions. It will be hard work, but, given enough 
energy and patience and skill, the children will survive it 
and will learn more of arithmetic than may be the case 
with listless teaching on a better plan. We might also 
start with the idea that every lesson should be a unit, 
and that in it should come every process of arithmetic, 
so far as this is possible, and we could stir up a good 
deal of interest in our "Unit Method." Or, again, we 
could begin with the idea that all action demands reac- 
tion, and that every lesson containing addition should 
also contain subtraction; that 6+4= 10 should be 
followed by 10 — 6 = 4 and 10 — 4 = 6; and that 
2 X 5 = 10 should be followed by 10 -^ 2 = 5 and 
10 -^ 5 = 2. By sufficient ingenuity a very taking 
scheme could be evolved, and the "Inverse Method" 
would begin to make a brief stir in the world. This in 
fact has been the genesis, rise, and decline of Methods; 
given a strong but narrow-minded personality, with 
some little idea such as those above mentioned; this 
idea is exploited as a panacea; it creates some little stir 



ARITHMETIC 327 

in circles more or less local; it is tried in a greater or less 
number of schools; the author and his pupils die, and 
in due time the Method is remembered, if at all, only 
by some inscription in those pedagogical graveyards 
known as histories of education. — Smith, Monograph 
on The Teaching of Arithmetic, 1909, page 23. 

632. Methods of teaching the concept of number. — 
It is unnecessary to outline in detail the first steps in 
teaching pupils to count. Most pupils have a concept 
of number long before they enter school; all they need 
is drill in wider application of their knowledge. Some 
teachers use splints in this drill; others use pencils, 
rulers, books, or the pupils themselves. The various 
devices are outlined in the next section, but through 
all the variety runs the uniform principle of concrete 
presentation. 

The first idea of number is never abstract. Slowly 
through the years of experience the mental process of 
abstraction produces the abstract concept of number. 
Four suggestions for concrete teaching are mentioned 
in the course of study. 

1. Scoring. This is simply a way of indicating the 
early impressions of number. The Arabic numerals are 
not so easily made as groups of vertical lines, thus: 

1 2^ 3 4 

/ //' /// ////• 

The drawing of such vertical lines to represent num- 
bers is called scoring. 

2. By measurements and comparisons. Actual use 
of pint and quart, five-cent piece and dime. Compari- 
son of groups of objects. 

3. Use of toy money in business operations. 



328 METHODS IN EDUCATION 

4. Use types in concrete problems. Here are the 
suggestive types: 

(1) If there are 3 apples in one group and 2 apples 
in another, how many apples are there in both? 

(2) If 3 apples are taken out of a group of 5 apples, 
how many apples remain? 

(3) If there are 2 plants in a row, how many plants 
are there in 3 equal rows? 

(4) If 2 plants are placed in a row, how many such 
rows are required for 6 plants? 

(5) If 6 plants are placed in 3 equal rows, how many 
plants are there in each row? 

" Exercises in counting should aid in column addition 
and in a mastery of the multiplication tables. Com- 
parisons and objective measurements should lead pri- 
marily to thought, rather than to over-much figure 
work. Oral work should precede and accompany all 
written work in every mathematical operation. Small 
numbers should be used in the illustration of principles." 

The counting in the first term is limited to counting 
by I's to 200, and lO's to 100. Later the pupils receive 
much drill in counting forwards and backwards by 
2's, 3's, 4's, 5's, etc. This is the process that gives 
the foundation for the tables in the' four fundamental 
operations. This paragraph relates to New York City 
practice. 

633. Concrete number operations, order of succes- 
sion. — We quote from the Scotch Memorandum. " The 
pupil must first learn the sequence of names in the 
number series, and be able to count a succession of 
objects one at a time. He should then be taught by 
concrete examples to perform the four operations with 
small whole numbers which may be slowly increased in 



ARITHMETIC 329 

magnitude as he advances. In addition to ordinary 
objects employed at this stage of the instruction it is 
useful to associate small numbers with geometrical 
forms, such as are seen on cards or dominos, as these 
forms not only give a picture of the number itself, but 
show the various ways in which it is made up." E.g., 
notice that in the form we have pictured all the 




possible ways in which seven can be made up. ''The 
common units of every-day life should be gradually 
introduced; e.g., the money units, the units of time, 
of length, of weight. The pupil should handle the coins 
and know their value. The clock should be used for 
the units of time. The units of weight should be used 
practically until the pupil has a clear idea of each unit 
and can give a fair estimate of a length or weight without 
actual measuring or weighing except to correct or verify 
his estimate. The units so introduced will give scope 
for the application of the four rules to problems of an 
every-day type." 

634. Summary of modes of concrete number opera- 
tions. — Notice that both measuring and counting are 
used in each of the devices in this summary. 

1. Counting visible objects, as chairs, birds, houses, 
children, apples, etc. 

2. Other objects, as tooth-picks, buttons, beads, pen- 
cils, fingers, etc. 

3. The abacus, cubes, blocks, squares, etc. 

4. Demonstrative devices, as distribution of papers, 
books, the marking off of positions at board, the paging 



330 METHODS IN EDUCATION 

of books, counting time on the clock, attendance records, 
thermometer; in home geography, counting houses, 
making maps, etc. 

5. Standard units, as gallon, pound, dollar, bushel, 
barrel, day, dozen, cubic foot, etc. Variety, practical 
units, ratios, and fractions from use of these. 

6. Number pictures made of dots, lines, etc.; dom- 
inos. 

7. In decimal scale, splints or tooth-picks in bundles 
of lO's and lOO's. 

635. The use of a book by pupils. — The safe rule for 
the time of introducing a text-book in any subject is 
this: A book should be introduced as soon as children 
are able to use it to their own advantage. The average 
child is not capable of reading well during the first term 
of school life and so there is little or no advantage for 
him in trying to use a text-book in arithmetic. For this 
reason, the work of the first term is largely oral, but as 
soon as the child is able to make any use of a text-book 
in arithmetic he should be given that privilege. The 
work in mathematics should not depend largely upon 
the hearing; it is another instance of multiple sense 
instruction. The interpretation of a printed problem 
requires more mental effort than the interpretation of a 
problem written on the board or dictated by the teacher. 
In the last two ways the pupil depends upon the assist- 
ance from the teacher. 

Devices for Drill in Primary Grades 

636. A distinction repeated. — All these suggested 
devices are only different ways in method; they are not 
methods in arithmetic. Devices of any kind are in- 
tended to attract and maintain attention. Curiosity, 



ARITHMETIC 331 

competition, and success are likely to secure interest. 
Different devices satisfy a desire for variety, and some 
of these have permanent value in being ready for use 
at any time. It is understood, of course, that these 
devices cover all the four fundamental operations — - 
addition, subtraction, multiplication, and division. 

637. Cards. — Number cards having the combina- 
tions on both sides of the card. 

638. Charts. — Charts made with rubber pen. Fig- 
ures large enough to be seen from any part of room. 

639. Mimeograph work. — Copies made by mimeo- 
graph admit many uses. Some copies may contain the 
same work for the whole class; other copies may have a 
few additional problems for the faster workers; a third 
kind may have different work for each pupil. 

640. Text-books. — A good text-book — no other 
kind should be used — has scores of examples suited to 
drill purposes. Use the book. Teachers may now 
secure separate books for each grade, and these are 
excellent supplements to the class text-book. 

641. Board. — Special work on the blackboard. The 
advantage is the probability of satisfying the exact 
needs of the class by adaptation; the disadvantages are 
temporary use and eye-strain. Every class has some 
pupils who cannot easily read blackboard work. 

642. Circle. — Figures outside circumference; num- 
ber in centre. 

643. Square. — Similar to arrangement in 642. 

644. Drawing. — Two vertical lines crossing two hori- 
zontal lines at right angles, giving places for nine figures. 
Vertical, horizontal, and diagonal drill. 

645. Dictation. — Dictation under limited time for 
answers. 



332 



METHODS IN EDUCATION 



646. Competition. — Competition under recorded time 
after definite assignment of work. 

647. Decimation. — This device uses ten as a basis 
in each of the four fundamental operations. Following 
is a table in counting: 



1 


2 


3 


4 


5 


6 


7 


8 


9 


10 11 


12 


13 


14 


15 


16 


17 


18 


19 


20 21 


22 


23 


24 


25 


26 


27 


28 


29 


Build to 


















100 101 


102 


103 


104 


105 


106 


107 


108 


109 



and then drill down and up. 



Decimations in Combinations 



0+1=1 


7+8 = 


15 


9+4 = 


1^ 


10+ 1 = 11 


17+8 = 


25 


19 + 4 = 


23 


20 + 1 = 21 


27+8 = 


35 


29+4 = 


33 


30+ 1 = 31 


37+8 = 


45 


39+4 = 


43 


40 + 1 = 41 


47+8 = 


55 


49+4 = 


53 


etc. 


etc. 




etc. 




Subtraction 






Multiplication 




99 — 6 = 93 






3X 6= 18 




89 - 6 = 83 






3X 16= 48. 




79 - 6 = 73 






3 X 26 = 78 




69 - 6 = 63 






3 X 36 = 108 




59 - 6 = 53 






3 X 46 = 138 




etc. 






etc. 





648. How to mark papers. — This topic brings up 
the question in regard to marking what is right or what 
is wrong, and also the use of per cents, letters, or other 
means of indicating the worth of answers. Another 
question arises here, namely, if the answer is incorrect, 



ARITHMETIC 333 

shall we allow anything for right methods of operation? 
In all problems accuracy is the first test of an answer. 
Answers are either right or wrong. The simple oral 
work cannot justly be marked upon any other basis. 
Later in the life of pupils it may be that the processes 
should be given some consideration, but the business 
demand for a correct answer is a criterion always to 
be kept in mind by the teacher. The use of letters or 
figures is a matter for individual decision. 

"649. The nature of the problems. — In speaking of 
the various kinds of elementary work we have insisted 
that the material should be adapted to the capacities 
of the pupils as well as to the needs of the course of 
study. These same principles apply in the primary 
arithmetic. Use problems that are adapted to the 
actual experience of the child. Such problems are the 
ones that produce interest at the same time that they 
give the requisite drill in the work. It is advisable to 
use problems that are related to the common forms of 
industry and other forms of life, but in the first grade 
it is probable that the interests of the children will 
require a simple presentation of experience in regard to 
games, toys, home life, etc., more than to the industrial 
phases of the community. Regarding the method of 
doing the work, both oral and written practice should 
be put into use as early as possible. Regarding abstract 
and concrete examples, both kinds should be used. 
Accuracy may result from using concrete problems 
alone, but rapidity can never be acquired without fre- 
quent drill on abstract numbers. Much of the work 
should, of course, be concrete, but as soon as the chil- 
dren are able to perform abstract number operations, a 
part of the daily drill should be devoted to rapid com- 



334 METHODS IN EDUCATION 

putation in abstract work. A few minutes each day 
through all the grades should be set aside for oral com- 
putation. It is suggested that in the written work a 
time limit be set so that each child may be judged accord- 
ing to his recitation. It is not expected that all pupils 
will be able to solve the same number of problems in 
the limited time. 

650. Opinions on drill. — Mechanical precision with 
abstract numbers can be accelerated, without detriment 
to the intelligence, by a well arranged summing up of the 
results already obtained in concrete cases. — Scotch 
Memorandum. 

Teachers are seriously attempting at the present time 
to co-ordinate the interests of the children, the needs 
of society, and the mathematical powers in each of the 
grades from the first year through the elementary school. 
■ — Smith, Monograph on The Teaching of Arithmetic, 
page 17. See Young, page 131. 

651. The fundamental operation. — The fundamental 
operation of arithmetic is counting. All other arith- 
metical operations are simply devices for speed by using 
remembered countings instead of going through the 
detailed. Herein is the hint furnished the teacher for 
the first lessons in arithmetic. Let the child construct 
gradually out of his countings his own tables of addition, 
subtraction, and multiplication, and fix them in his 
memory. — Harris, Ed. Rev., Vol. 9, page 243. 

652. Hint from experience of the race. — It is inter- 
esting to reflect that the concrete problems that they 
differentiate as addition, subtraction, multiplication, 
measurement, and partition, came to primitive man 
unclassified ; and he solved them all by counting without 
realizing that they were of different classes. Take three 



ARITHMETIC 335 

illustrations, the second and tlie third together being 
the inverse of the first. 

1. If a wild savage chief wants to distribute 6 fresh- 
water clams apiece to 4 warriors, how many must 
he have to distribute? 

2. If a chief wants to deal out 18 clams to as many 
as he can, giving 6 to each, how many will receive clams? 

3. If he wishes to distribute 18 clams equally to 3 
meUj how many will each receive? 

All of the intricacies and mysteries of measurement 
and partition are wrapped up in the last two problems, 
but the savage chiefs solved them all by counting, and 
so can the small boy. The practice is justified also by 
the culture epoch theory of education. 

Addition 

653. A kind of counting. — This is another applica- 
tion of counting. Some writers speak of addition as a 
synthesis of the elements of knowledge gained in the 
first number concepts. But addition is so closely related 
to the first work in counting that it is not necessary to try 
to set limits between the two kinds of mental operations. 
Counting by I's is addition; and surely the counting by 
2's, 3's, etc., is giving results in addition, whether called 
so or not. 

The first addition tables are the combinations of num- 
bers of one order with 1 and 2 : 

123456789 23456789 
iiiiiiiil 22222222 

sums found by counting objects; the value of each num- 
ber and of each combination, as 3 and 2 are 5, 2 and 3 



336 METHODS IN EDUCATION 

are 5, should be recognized at sight without counting 
the combinations memorized. 

A continuation of the drill in addition gives forty-five 
combinations of digits, taking two figures in each com- 
bination. 

654. The forty-five combinations. — Following is the 
complete list as it is taught in the first two years of 
school: 



1 


2 


3 


4 


5 


6 


7 


8 


9 


1 


1 


1 


1 


1 


1 


1 


1 


1 




2 


3 


4 


5 


6 


7 


8 


9 




2 


2 


2 


2 


2 


2 


2 


2 






3 


4 


5 


6 


7 


8 


9 






3 


3 


3 


3 


3 


3 


3 




• 




4 


5 


6 


7 


8 


9 








4 


4 


4 


4 


4 


4 




4 






5 


6 


7 


8 


9 










5 


5 

6 
6 


5 

7 
6 

7 
7 


5 

8 
6 

8 

7 

8 
8 


5 

9 
6 

9 

7 

9 

8 

9 
9 



655. Automatic habits. — After all of these combina= 
tions whose sum is 10 or less are thoroughly memorized, 



ARITHMETIC 337 

and special attention has been given to the combinations 
making 10, then proceed as follows: 

1. 10 + 1 = 11, 10 + 2 = 12, 10 + 3 = 13, etc., to 
10 + 10 = 20. 

2. Then in any such sum as 13+ 5, proceed thus: 
13 + 5 = 10 + 3 + 5 = 10+8. 

3. To pass from a number in the first decade to a 
number in the second decade, as 8+7, proceed thus: 
8+7=8+2+5= 10+5= 15. Or after special 
attention has been given to series 6+6, 7+7, 8+8, 
9+9, the following method may be used: 8+7 = 
1+7+7= 1+14= 15. 

These are methods of using known combinations to 
discover new combinations in constructing the tables 
without taking the trouble to count up. A combination 
of methods is not only possible but desirable, as the 
ultimate aim is to suppress the intermediate and secure 
the result in one step automatically, which can be more 
easily effected if the intermediate step is variable. 
— Scotch Memorandum. 

656. Two fundamental facts. — As soon as the sum 
of two numbers involves the process of ''carrying," 
two fundamental facts must be taught: 

1. Ten units make one ten. 

2. Place gives value to a figure. 

The practice in counting by lO's is a preparation for 
both these facts, and the drill on addition giving sums 
from 10 to 20 will impress the truth. 

657. Decomposition. — When the sum is 20 or more, 
it may be helpful to show units and tens by decomposi- 
tion. This process is not approved by some educators, 
but it is inserted here for the use of those who wish to 
teach it. 



338 METHODS IN EDUCATION 

1. 16+' 5= ? Then 10 units 

16 = 1 ten + 6 units + 6 units 16 

= 10 units + 6 units. + 5 units + 5 



21 units. 21 ans. 

2. 24+ 13 = ? Then 20 units 
24 = 2 tens + 4 units + 4 units 

13 = 1 ten + 3 units. + 10 units 24 

+ 3 units +13 

37 units. 37 ans. 

3. 87+36= ? Now we meet the fact that ten tens 
make one hundred. 



87 
+ 36 



ds 


tens 


units 




8 


7 




3 


6 




11 


13 


1 


2 


3 



123 ans. 



658. Algorisms. — This is a word relating to the form 
of work, i.e., the arrangement. The column or vertical 
arrangement is preferred, since so much column addi- 
tion is required in life. The psychological habit of 
vertical addition is, therefore, more important than the 
habit of horizontal addition. Both are combined for 
proof in the grammar grades. The proof of addition in 
the primary grades is made by reversing the order of 
adding. If the first process was from the bottom to 
the top, then for proof begin at the top and add down. 

Equation. — The horizontal form of expressing an 
example in addition gives an equation, thus: 

32+19= 51. 
In other words, the expression of equality in mathematics 
is an equation. The part before the sign of equality is 



ARITHMETIC 339 

the first member; the part after the sign of equahty 
is the second member. The equation is a kind of 
algorism. 

659. Laws or principles of addition. 

1. Only like numbers can be added. 

2. The sum is the same in kind as the addends. 

3. If the like orders of units be added separately, the 
sum is the sum of all the numbers added, since the 
whole is equal to the sum of all its parts. 

4. If the sum of the units of any order contains units 
of a higher order, these higher units must be combined 
with units of like order. 

Subtraction 

660. Relation to addition. — As addition is consid- 
ered synthesis in counting, subtraction is analysis in 
counting. Addition and subtraction may be taught 
together, using subtraction as the inverse of addition. 
Sticks, pencils, and other concrete devices are used as 
material, and the child measures the difference in the 
groups by counting. Considerable facility in rapid sub- 
traction should be secured in the easy combinations 
before introducing the necessity of " borrowing." De- 
composition will be used again to explain the relations of 
units, tens, and hundreds in subtraction. It is only one 
step from the known process in addition. 

661. Decomposition to explain borrowing. 

35- 18=? 

35 = 3 tens + 5 units = 30 + 5 = 35 

= 2 tens + 15 units = 20 + 15 = 35 35 

18 = 1 ten + 8 units = 10 + 8 = 18 - 18 

1 ten + 7 units = 10 + 7 = 17 17 ans. 



340 METHODS IN EDUCATION 

662. Equal addition to explain borrowing. — A few 

years ago the method of equal additions was widely 
used among the disciples of Pestalozzian number. It 
is not used much today, although the axiom still holds; 
namely, If equal numbers be added to unequal numbers, 
the difference between the unequal numbers remains 
unchanged. 

35 - 18 = ? Or 35 
- 18 



35 + '10 = 3 tens + 15 units = 30 + 15 = 45 
18+10=2 tens + 8 units = 20 + 8 = 28 

1 ten + 7 units = 10 + 7=17 

35 

-18 
35 - 18 = 17 ans. Or 17 ans. 

This operation has combined the use of decomposi- 
tion with equal additions to make the number of units 
in the minuend greater than the number of units in the 
subtrahend. 

663. Complementary addition in subtraction. — This 
method is an application of addition, thus: 

764 

- 478 



286 ans. 

Instead of saying 8 from 14, we observe that 6 added 
to 8 will make 14, and the process becomes 

8 + 6 = 14, 8 + 8 = 16, 5 + 2 = 7. 
This method is mentioned by Smith in the next para- 
graph. 



ARITHMETIC 341 

664. Four ways of performing subtraction. — 

In subtracting 297 from 546, we have the two 546 
old plans, both dating from the time of the 297 
earhest printed text-books, at least. 249 

The calculation is substantially this: 

(1) 7 from 16, 9; 9 from 13, 4; 2 from 4, 2; or 

(2) 7 from 16, 9; 10 from 14, 4; 3 from 5, 2. 
But we have also a more recent plan: 

^3) 7 and 9, 16; 10 and 4, 14; 3 and 2, 5. 

To this might be added a fourth plan, which has 
some advocates: 

(4) 7 from 10, 3; 3 and 6, 9; 9 from 10, 1; 1 and 3, 4; 
2 from 4, 2. 

All four of these plans are easily explained, the first 
rather more easily than the others. But the third has 
the great advantage of using only the addition table in 
both addition and subtraction, and of saving much 
time in the operation. It is the so-called ''Austrian 
method" of subtraction. The fourth plan, while a 
very old one and possessed of some good features, 
is so ill adapted to practical work as to have no 
place in the school. It is hardly necessary to say 
that the old expressions ''borrow" and "carry" in 
subtraction and addition are rapidly going out of use; 
they were necessary in the old days of arbitrary 
rules, but they have no advocates of any prominence 
today. — Smith, The Teaching of Elementary Mathe- 
matics, page 121. 

665. Principles of subtraction. 

1. Only hke numbers can be subtracted. 

2. If the units of each order in the subtrahend be 
taken separately from the units of hke order in the 
minuend, the sum of the differences equals the entire 



342 METHODS IN EDUCATION 

difference of the given numbers. Axiom: The whole 
equals the sum of all its parts. 

3. If both minuend and subtrahend be equally in- 
creased the difference will not be changed. 

666. Proof of subtraction. — Add difference and sub- 
trahend; or subtract difference from minuend to get 
subtrahend; or cast out 9's. 

Multiplication 

667. Special case of addition. — This process is 
treated as synthesis in taking one number a certain 
number of times. Multiplication is a short form of 
addition, or, more strictly speaking, is a special case 
of addition, namely, that in which the several addends 
are equal; and in which consequently another memory 
device, namely the multiplication table, is possible. 

668. Counting. — For first steps, arrange and count 
concrete objects as in addition and subtraction. 

669. Decomposition. — Use decomposition again to 
explain multiphcation by one figure. 

28 = 20 + 8 
28 20 X 3 = 60 

3X 8 X 3 = 24 

28 X 3 = 84 

Decomposition to explain multiplication by two 
figures. 

67 67X 3= 201 

23 X 67 X 20 = 1340 

67 X 23 = 1541 

This work may be arranged in another form: 



201 
1340 



ARITHMETIC 343 

Multiplying by 3 units we have 201 units; gy 
multiplying by 20 units we have 1340 units. 23 X 
The sum of these partial products is 1541 
units. 

Since 1340 units = 134 tens, we omit the 
cipher, and write 134 as tens. This shorter 
process gives the final form. 

thousands hundreds tens units 

6 7 

2 3X 

2 1 

13 4 



670. Justification. — These three examples are justi- 
fied by the third principle of multiphcation in section 
675, or rather by a principle of which that third prin- 
ciple is a special case, namely, that the product of a 
number by the sum of two other numbers is equal to 
the sum of the products obtained by multiplying that 
number by each of those numbers separately. This is 
the distributive law of multiplication, and is an axiom 
or a fundamental assumption verified by all experience. 
It is useful, in impressing this truth, to multiply by 20 
first. The method is just as easily grasped by gy 
the small child. It impresses the fact that in 23 V 
multiplying 67 by 23 we are multiplying by 20 rrrr 
and by 3. It has the advantage of doing the » 

most important part of the work first — a 

procedure that is always commendable. In 
fact, the method is insisted on for the last named reason 
in Elson and Short's First Book in Mathematics just 
published by Heath. 



344 METHODS IN EDUCATION 

671. Multiplication by factors. — Variety is one 
advantage, a means of proof is another, and a practice 

3546 in analysis of numbers is a third. Another 

X 24 justification is the associative law of multipli- 

Qc^^g cation. This process illustrates the law: 3546 

^ g X 24 = (3546 X 6) X 4 = (3546 X 4) X 6 = 

T-— — 3546 X (4 X 6). This is another important 

^ law which may be regarded as axiomatic in 

character and a fundamental law of the science 

of number. 

672. Justification by commutative law. — The com- 
mutative law is equally important and good for varietj^, 
for proof, and for knowledge of the properties of number. 
According to the first principle in section 675, the mul- 
tiplicand and multiplier may be interchanged. 

67 23 

23 X 67 X 

201 161 

1340 138 



1541 1541 

673. Commutation, association, and distribution. — 

A statement of the three laws may be helpful to some 
students. The laws relate to arrangement and analysis 
of numbers. 

The law of commutation says the product is the same, 
independent of the order in which the numbers are 
multiphed. 

5X6X7=7X6X5=6X7X5. 
Likewise in addition. 

5+6+7=7+6+5=6+7+5. 

The law of association, applied to multiplication, says 
that the use of brackets makes no difference in the 
process. 



ARITHMETIC 345 

2X3X5=6X5=10X3=15X2. 
But the use of brackets in combined addition and sub- 
traction does make a difference. 

5 + 6 X 7 = 47 
(5 + 6) X 7 = 77. 
The law of distribution uses analysis by a kind of 
decomposition of numbers. 

5=2+3. 
Then 4X5=4X2+4X3= 20. 

a{h + c) = a6 + ac. 
The product of the sum of two numbers by a third 
equals the sum of the products of the numbers by the 
third number separately. 

3(5 +4) =3X9=3X5+3X4. 
The important apphcation is 

25 X 33 = 25 X 3 + 25 X 30. 
674. Multiplication tables: mode and order of learn- 
ing. — Learning these tables by the memory process 
alone is condemned. All the work in counting by Ts, 
2's, 3's, etc., is a preliminary preparation. The com- 
binations in the four operations are another aid; and 
then the use of acquired knowledge in measuring with 
foot-rule, yard-stick, toy money, pints, quarts, etc. — 
all help the pupils to construct the tables out of personal 
experience in counting and measuring. 

The order of learning the tables is not that of the old 
books. An easy order is as follows: lO's, 2's, 5's, 4's, 
8's, 3's, 6's, 9's, 7's. This order starts with lO's as the 
easiest; then the 2's are not difficult; the 5's easily unite 
with the lO's and the 2's; so, too, the 4's and the 8's, 
and then 3's, 6's, and 9's. The 7's are not closely related 
with any other table; but by leaving the 7's till the 
last, all the combinations in the 7's are then covered by 



346 METHODS IN EDUCATION 

the other tables. Other opinions favor a different order 
of procedure, but McMurry upholds this one. 

675. Principles of multiplication. — When either fac- 
tor contains more than one figure, the principles are as 
follows: 

1. The product is the same, whichever factor is used 
as multiplier. 

2. If one factor be units of the first order, the product 
will be the same in kind as the other factor. 

3. If units of each order in the multiphcand be taken 
separately as many times as there are units in the mul- 
tiplier, the sum of the products equals the entire product 
of the given numbers. 

676. Proof of multiplication. — Divide product by 
multiplier to get multiphcand; or invert order of factors 
and multiply; or cast out 9's. 

677. Concrete and abstract numbers in multiplication. 
— This is the place for discussion of terms concrete 
number and abstract number. A concrete number is a 
number with the name of the unit designated. MuU 
tiplicand may be either concrete or abstract, but 
multiplier must be abstract. Even if multiplicand is ab- 
stract, the multiplicand and multiplier must be different 
kinds of numbers, i.e., refer to units of different sorts; 
the multiplicand refers to units of some sort, though 
the sort is not designated, and the multiplier to units 

• not of the same sort, but to repetitions of the group 
represented by the multiplicand. 

Illustration 

If 3 pencils cost 2 cents apiece, how much will the 
3 cost? Answer, 3 times 2 cents. Is it 3 pencils 
times 2 cents? Absurd; not 3 pencils times 2 cents. 



ARITHMETIC 347 

but 3 times 2 cents, because the 2 cents must be repeated 
as many times as there are pencils. 

Even in concrete problems, such as that just discussed, 
multiplication is commutative as is shown by the fol- 
lowing analysis. If the 3 pencils had cost 1 cent 
apiece, the 3 would have cost 3 cents; but, since each 
costs 2 times 1 cent, the three will cost 2 times 3 cents. 
It appears, then, that multiplier and multiplicand may 
be interchanged, but that the multipUer in becoming 
multiplicand takes on the concrete character of cents 
and the multiplicand in becoming multiplier loses its 
concrete character and becomes times. 

, Division 

678. Nature of division. — An analytic process, the 
inverse of multiplication; i.e., the process of finding one 
factor when product and the other factor are given. 
Division may also be regarded as repeated subtraction 
of divisor from dividend. 

679. Measurement and partition. — In speaking of 
product in the preceding paragraph, product is the 
dividend and the known factor may be either multi- 
plicand or multiplier. As emphasized in section 677, 
the multiplicand is presumably concrete, the multiplier 
always abstract, and at any rate numbers referring to 
different kinds of units. Arising from these conditions, 
two cases of division may be distinguished: (1) measure- 
ment, or that in which a number, the multiplicand, is 
repeated in a number of the same sort, the product, and 
in which the problem is to find how many times, the 
multiplier; (2) partition, or that in which the number 
of times is given, and the problem is to find the multi- 



348 METHODS IN EDUCATION 

plicand. The first case is like physical measurement 
and hence the name. 

In the second case, partition, if the operations were 
to be performed actually instead of symbolically it 
would be seen to be measurement after all. Distrib- 
ute 52 cards to four people and find size of each 
pile. The problem is of course to find one-fourth of 52, 
i.e., partition, but the method is to deal a card to each 
of the four people and then determine how many times 
this process of dealing out four cards from the 52 can 
be repeated, which process is evidently measurement. 
Hence, McLellan and Dewey contend very strenuously 
that there is no such thing in arithmetic as partition. 
(Psychology of Number, page 123.) 

680. Short division. — Short division is only the in- 
verse of the combinations in multiplication. 

Long division. — Long division by decomposition 
(distributive law). 



684 



2=? 



600^ 


-2 = 


300 


80- 


-2 = 


40 


4- 


-2 = 


2 


684- 


1-2 = 


342 ans. 


Other forms. 




342 


2)684(342 
6 

8 




• 2)684 
6 

8 


8 
4 




8 
4 


4 




4 



A more difficult example. 



ARITHMETIC 349 

We say 674 = 6 hundreds, 7 tens, 4 units. 2)674(337 

6 hundreds -f- 2 = 3 hundreds. Bring down 6 

7 tens; 7 tens -r- 2 = 3 tens and 1 ten re- 7 
maining. 1 ten and 4 units = 14 units; 14 g 
units -i- 2 = 7 units. The quotient is 3 hun- ^ 
dreds, 3 tens, 7 units, or 337. ^^ 







681. Division by factors (associative law). 

3864 -^ 24 = ? 
4 )3864 
6)966 



161 ans. 

682. Laws or principles of division. 

1. Dividing a number by one of its factors gives the 
other factor. 

2. When the divisor is an abstract number, the 
quotient and the dividend are Uke numbers. 

3. When the dividend and the divisor are hke num- 
bers, the quotient is abstract. 

683. Proof of division. — To prove division, multiply 
quotient and divisor to reproduce dividend. 

684. Grube method : characteristics, advantages. — 
The leading characteristic of this method is that it tries 
to teach the four fundamental processes with each num- 
ber before the next number is taken up. It is an appli- 
cation of the old idea of teaching in ^'concentric circles.'' 
Advantages claimed: simplicity and thoroughness. 

. 685. Objections to the Grube method. 
1. A unit not a fixed thing. The natural beginning 
of number is a whole — needing measurement, while 
Grube says that one thing is the natural beginning. 



350 METHODS IN EDUCATION 

2. Different processes are not equally difficult. 

3. Free range among higher numbers excluded. 

4. Synthetic only; memory drill. 

These four objections are from McLellan and Dewey. 
The following are from Smith, page 91 : 

1. It carries objective illustration to an extreme, 
studying numbers by the aid of objects for three years, 
until 100 is reached. 

2. It attempts to master each number before taking 
up the next, as if it were a matter of importance to know 
the factors of 51 before the child knows anything of 75, 
or as if it were possible to keep children studying 4 
when the majority know something of 8 before they 
enter school. 

3. It attempts to treat the four processes simultane- 
ously, as if they were of equal importance or of equal 
difficulty, which they are not. 

686. Speer method. — This is an attempt to teach 
concretely that ratio is number. Judgments of relative 
magnitude are secured by using the type forms — cubes, 
prisms, etc. — in getting the concept of number. Criti- 
cism: Not a direct use of materials in daily life; from 
complex to simple. It should be noted, however, that 
this method recognizes the acceptable ratio idea of num- 
ber and attempts to introduce the ratio idea earlier than 
has been the case. Smith seems to favor this earlier 
introduction (page 105). 

687. Graphic methods. — Graphic methods include 
all objective ways of aiding visualization, such as writing, 
drawing, pictures, cubes, etc. Technically, a graph is 
a line representing variations of temperature, price, 
population, class standings, etc. 

Illustration. Add J and |. 



ARITHMETIC 



351 



1^3 
2 6 



2~^3 6 6* 

Properties of Number for Primary Grades 

688. Extent of work. — Certain properties of number 
are easily grasped by children of the earlier grades and 
may be profitably taught to them. The distinctions of 
odd and even numbers, and of prime and composite 
numbers, and the tests of divisibility by 2, 3, and 5, are 
of this class. Also definitions of factor, product, power, 
root. 

689. Odd and even. — Study the numbers / // /// 
////, etc. Which of them are capable of being grouped in 
pairs? Such are even, the rest are odd. What is the 
appropriateness of the names? 

690. Prime and composite. — Represent the several 
numbers by scoring, as in the preceding section. Some 
of them, as 1, 2, 3, 5, 7, cannot be divided in any way 
into equal groups, but 4 (// //) may be divided into two 
groups of two each, 6 (/// ///) or (// // //) into two 
groups of three or three groups of two, 9 (/// /// ///) 
into three groups of three. Those of the first class 
we call prime, those of the second, composite numbers. 
What is the appropriateness of the names? 



352 METHODS IN EDUCATION 

691. Divisibility. — State how to tell without dividing 
whether 2 will be exactly contained in a number? The 
answer is contained in the definition of even number 
as given in section 689. As it happens, these numbers 
always end in 2, 4, 6, 8, or 0. 

Study the multiplication table of 5's and, noticing 
how the numbers all end, frame a statement telling what 
numbers are divisible by five. Verify. 

Study the numbers 10, 11, 12, 13, 14, 15, 16, 17, 18. 
Which are divisible by 3. Is it also true that the sum 
of the digits of those numbers is divisible by 3? What 
is true in this respect of the other numbers? Make a 
general statement summarizing the observations. Verify. 

Properties of Number for Higher Grades 

692. Induction and deduction. — The examples in the 
preceding section illustrate the application of the induc- 
tive method to the discovery of the principles of arith- 
metic, and at the same time show that the formal steps 
of instruction are simply the steps in inductive reason- 
ing. It is well established that in the earlier years, at 
least, the principles of arithmetic should be arrived at 
inductively. But on the other hand, arithmetic {i.e., 
the science or theory of number) may be treated as a 
purely deductive science, and in the later grades it is 
well to give the children some notion of that truth. 
Properties of number is a topic well adapted for that 
purpose. 

693. Commutative, associative, and distributive laws. 
— See section 673. 

694. Other general properties. 

1. If a number is contained exactly in two numbers, 
it is contained exactly in their sum or difference. 



ARITHMETIC 353 

This law is probably as nearly axiomatic as any law 
can be. The following will illustrate the necessary char- 
acter of its truth: 



a h c b-\- c 

If a is exactly contained in h and also in c it is evidently 
exactly in 5 + c. 

» 2. If a number is exactly contained in another it is 
exactly contained in any multiple of that other number. 

This is a corollary of number 1. 

3. If a number exactly contains two numbers, prime 
to each other, it contains their product. 

If 24 contains 3 and 4, it contains 12. 

This rule is a corollary of the associative law of mul- 
tiplication; because if 24 contains 3 and 4 and some 
other factor a, then 24 = 3 X 4 X a. Therefore 24 = 
(3 X 4)a by associative law. 

These laws are general because they are true of num- 
bers as such, while the tests of divisibility are true only 
for our particular system of notation. The whole body 
of principles of number may, moreover, be derived 
deductively from these general properties as geometry 
is derived from a few axioms and definitions. 

695. References. — For more exhaustive treatment 
of the properties of number, see Chrystal's Algebra 
Part II, Chapter 35; any approved college algebra; 
Encyclopedia Brit., Theory of Numbers. 

696. Application : tests of divisibility. — The tests of 
divisibility illustrate the application of the laws of 
properties of number as expressed in our decimal nota- 
tion. A number is divisible 

By 2, if it ends in 0, 2, 4, 6, 8. 



354 METHODS IN EDUCATION 

By 3, if the sum of its digits is divisible by 3. 

By 4, if the number represented by the two digits at 
the right is divisible by four. 

By 5, if it ends in or 5. 

By 6, if divisible by 2 and by 3. 

By 8, if the number represented by the three digits 
at the right is divisible by 8. 

By 9, if the sum of its digits is divisible by 9. 

By 10, if it ends in 0. 

By 12, if it divisible by 3 and by 4. 

By 7 and 11, actual division test. 

697. Types of demonstration. — We may, as stated 
before, satisfy ourselves of the truth of these proposi- 
tions by inductive study, but deductive demonstration 
is more satisfactory to the mature mind, because it not 
only satisfies us of the truth of the proposition but shows 
that the truth is a necessary logical consequence of 
more fundamental truths. For example, take tests of 
divisibihty by 3 and 12. 

698. Test by 3. — Let a, h, c, d, and e represent the 
digits of the number and assume that the sum of the 
digits a+6+c+<i+e, etc., is divisible by 3. 

a + 106 + 100c + lOOOd + etc. represents the num- 
ber. 

Prove a + 106 + 100c + lOOOf^ + etc. is divisible by 3. 

Proof: Syllogism 1 

Major Premise. If a number is contained in another 
number, it is contained in any multiple of that number. 

Minor Premise. 3 is evidently contained in 9, 99, 
999, etc. 

Conclusion. 3 is contained in 96, 99c, 999c?, etc. 



ARITHMETIC 355 

Syllogism 2 

Major Premise. If a number is contained in each of 
several numbers, it is contained in their sum. 

Minor Premise. 3, as just proved, is contained in 
9b, 99c, 999d, etc. 

Conclusion. 3 is contained in 96 + 99c + 999d, etc. 

• Syllogism 3 

Major Premise. If a number is contained in each of 
two numbers, it is contained in their sum. 

Minor Premise. 3 is contained ina+6+c+f? + 
etc, by hypothesis and in 96 + 99c + 999d + etc., as 
just proved. 

Conclusion. 3 is contained in a + 106 + 100c + 
1000c/ + etc. 

Test by 12. — A number is divisible by 12 if divisible 
by 3 and 4. 

Proof: Syllogism 

Major Premise. If a number is divisible by each of 
two numbers, prime to each other, it is divisible by 
their product. 

Minor Premise. The number in question is divisible 
by 3 and 4, numbers prime to each other, by hypothesis. 

Conclusion. The number is divisible by 12, the 
product of 3 and 4. 

699. Frequent use of syllogism. — Aside from the 
specific illustrations just given, the syllogism is fre- 
quently used although students may not be conscious 
of using this form of reasoning. Bailey discusses this 
topic in the N. E. A. Report, 1905, page 384. He calls 



356 METHODS IN EDUCATION 

the process of reasoning traduction. He says: " Three 
statements are involved. The major states the relation 
between the required term and the given term; the 
minor states that the given term is equivalent to a 
second term; and the conclusion makes the same state- 
ment involving the second term which the major premise 
makes involving the first term. The conclusion is 
valid, because, in any proposition, a term may be 
replaced by a second term, provided the second term is 
equivalent to the first. " 

Illustration. If 1 apple costs 3 cents, how much will 
5 apples cost? 

Major. ''The cost of 5 apples" is 5 times "the cost 
of 1 apple." 

Minor. "The cost of 1 apple" is "3 cents." 
Conclusion. The cost of 5 apples is 5 times " 3 cents." 
It is customary to abbreviate the argument by the 
omission of one of the premises. In some localities, the 
major is omitted, giving the form: ''Since the cost of 1 
apple is 3 cents, the cost of 5 apples is 5 times 3 cents; " 
in others, the minor is omitted, giving the form: "Since 
the cost of 5 apples is 5 times the cost of 1 apple, the 
cost of 5 apples is 5 times 3 cents." 

The argumentative power developed by analysis is 
strongly commended by Smith in his monograph of 
1909, page 11. 

Divisors 

700. Common divisors and factors: highest common 
factor. — The terms, greatest common measure, highest 
common factor, greatest common divisor, are inter- 
changeable, each preferable under certain conditions, the 
first preferable on the ground of its implied concreteness. 



ARITHMETIC 357 

The definitions of the terms, factor, divisor, measure, 
common factor, greatest common measure, etc., are 
obvious, but it is very important to good teaching that 
they be insisted on and carefully elaborated. Ridicu- 
lous mistakes are committed because children and some- 
times teachers do not reflect that the adjective common 
implies at least two things, and that a common factor 
is a factor of each of at least two numbers. 

Finding Highest Common Factor 

701. By observation. — Derive greatest common 
divisor directly from the definition; e.g., 24 and 36. 

List of exact divisors of 24 is 2, 3, 4, 6, 8, 12, 24; 
and that of 36 is 2, 3, 4, 6, 9, 12, 18, 36. Evidently 
2, 3, 4, 6, and 12 are common divisors and 12 is evidently 
greatest common divisor. 

This method of treatment is important because it 
applies and enforces the definitions and also because it 
is practically the method that we generally employ. 
We mentally go over the lists of common factors and 
select the greatest without taking the trouble to resort 
to any of the following methods. 

702. By product of prime factors. — To find greatest 
common divisor, resolve each of the several numbers 
into prime factors and find product of the common 
prime factors. 

1. We may lead to the discovery of the principle by 
inductive approach, thus: 

Numbers All the divisors Prime factors pi-jme'^Stors ^- ^- ^• 



24 

36 



2, 3, 4, 6, 8, 12, 24 
2,3,4,6,9,12,18,36 



2, 2, 2, 3 
2, 2, 3, 3 



2,2,3 



12 



358 METHODS IN EDUCATION 

From an inspection of all the divisors we perceive 
that 12 is the G. C. D. ; from an inspection of the prime 
factors we perceive that 12 is the product of the common 
prime factors. We therefore infer that the G. C. D. is 
the product of common prime factors. 

Here we have the steps, preparation, presentation, 
comparison, and generalization, of the orthodox lesson. 
But the generalization rests on too slender a foundation. 
It should be verified by treating other numbers in the 
same way and then widely applied. 

2. The same law may be derived deductively from 
general properties of number as follows: We use here 
the usual arrangement of demonstration into statement 
and reason. The statement is the conclusion, reason 
the major premise, and the minor premise must be 
inferred from the context. 

Statement 1. The product of the common prime 
factors of a number is exactly contained in each. 

Reason for 1. If a number contains each of two or 
more numbers prime to each other, it contains their 
product. 

Statement 2. This product is the largest number 
contained in each and therefore the G. C. D. 

Reason for 2, If there were a common divisor larger 
than this product, it would have to be either prime or 
composite. It could not be prime because this product 
contains all of the common prime factors. If composite, 
all of its factors would be common, but this product 
contains all of the common prime factors. 

703. By continued division. — A third method, appli- 
cable when the divisors of the numbers cannot be readily 
found, is the method of continued division. 

Divide larger by smaller, then the smaller by the 



ARITHMETIC 359 

remainder and so on until a remainder is found that will 
be exactly contained in the preceding remainder. This 
last remainder is the G. C. D. 

Find the G. C. D. of 849 and 1132. 
849)1132(1 283 is G. C. D. of 849 and 1132. 

849 

283)849(3 
849 

Graphic Illustration 

Find greatest common measure of lines AB and CD. 
A E B EB is greatest 

~ ' common measure 

C D of ^B and CD. 

Proof Statement 1. Greatest common measure of 
AB and CD will be contained also exactly in EB. 

Reason for statement 1. If a quantity is exactly con- 
tained in each of two quantities, it is contained in their 
difference. 

Statement 2. Therefore G. C. M. oi AB and CD is 
not greater than EB. 

Reason for 2. Evident because contained exactly in 
EB. 

Statement 3. EB is exactly contained in CD. 

Reason for 3. Found to be so by actual trial. 

Statement 4. EB is therefore contained in AB. 

Reason for 4. Being contained in AE (the equal 
of CD) and itself (EB) it must be contained in their 
sum. 

Statement 5. Therefore EB is a common measure 
oi AB and CD. 

Reason for 5. Statements 3 and 4. 

Statement 6. Therefore EB is G. C. M. 



360 METHODS IN EDUCATION 

Reason for 6. It is a common measure and the 
G. C. M. is not greater. (Statement 2.) 

This proof is an example of the truth that the deduc- 
tive as well as the inductive method is capable of objec- 
tive treatment. It is identical with Euclid's treatment 
in Prop. 2, Bk. VII (b.c. 300). Many educators ehminate 
this proof from both arithmetic and elementary algebra. 

Multiples 

704. Definitions. — A multiple of a number exactly 
contains that number. A common multiple of two or 
more numbers exactly contains each of the numbers. 
The least common multiple of two or more numbers is 
the least number that exactly contains each of the 
numbers. 

Illustrations. The multiples of 6 are 6, 12, 24, 30, 
36, etc. The multiples of 9 are 9, 18, 27, 36, etc. Select 
the common multiple of 6 and 9 and it will be L. C. M. 

Finding Least Common Multiple 

705. First method. — Find L. C. M. of several num- 
bers by writing out the list of multiples of each, and 
then taking the first multiple common to the several 
numbers. This is the method of observation. 

706. By multiplying prime factors. — The process of 
finding a multiple is simphfied by finding the prime 
factors of each number and then multiplying those 
factors. The least common multiple is the product of 
the prime factors, each taken the greatest number of 
times it is found in any one of the numbers. This 
principle may be proved inductively and deductively. 

1. Inductive proof. The prime factors of 6' are 2 
and 3; of 9, 3 and 3. But we have already ascertained 



ARITHMETIC 361 

that the L. C. M. is 18, which is evidently the product 
of the factors of 9 multiphed by 2, the factor of 3 not 
found in 9. Hence we assume the principle stated and 
proceed to verify it by other numbers. 

2. Deductive proof. The principle may be shown to 
be a necessary logical consequence of the principle that 
if a number contains any number it contains each factor 
of that number. 

707. Factoring by inspection. — This process follows 
easily as a result of knowing the combinations. 

Find L. C. M. of 20, 30, and 70. 
20 = 2 X 2 X 5 
30 = 2 X 3 X 5 
70 = 2 X 5 X 7 
The factors common to all the numbers are 2 and 5. 
The factors not common to some of the numbers are 
2, 3, and 7. Hence, according to the rule in 1, L. C. M. 
= 2X5X2X3X7= 420. 

708. Actual division. — Find L. C. M. of 15, 60, and 



75. 



15 


60 


75 


3 


12 


15 


1 


4 


5 




2 


5 



Hence, L. C. M. = 5X3X2X2X5= 300. 

709. By aid of G. C. D. — This way is used when the 
numbers are not easily factored by inspection. 
1. Find greatest common divisor. 
849)1132(1 
849 

283)849(3 
849 



362 METHODS IN EDUCATION 



2. Find other factors. 



283 



849 1132 



3 4 

3. Multiply. 283 X 3 X 4 = 3396 L. C. M. 

Fractions 

710. Common Fractions. — Familiarity with com- 
mon fractions is a natural result of the gradual intro- 
duction of this work. Fractional parts are introduced 
during the first year in arithmetic, and then the passing 
from the known, i, J, i, etc., to the related unknown in 
larger fractions is going from the simple to the complex. 
Addition, subtraction, and division of fractions are best 
explained by reducing to common denominators. The 
method of common denominators may not be the usual 
one in division of fractions, but it is a logical step since 
the children become familiar with the meaning of com- 
mon denominators in addition and subtraction. It may 
be needless repetition to say that all of the introductory 
practice in common fractions should be based upon the 
use of objects with which the children are familiar. It 
is more necessary because the symbol for the fraction 
is a clumsy, comphcated affair, through which it is 
much more difficult to get hold of the concept of the 
fraction than through objective illustration. 

In the fraction itself there is nothing more difficult 
than in the group. Five-tenths is as easy as five tens. 

" The relations of magnitudes should, so far as pos- 
sible, be represented to the eye. The fundamental oper- 
ations should not only be performed symbolically by 
the digits, but practically, by joining fines together, 
dividing them into parts, and combining the parts in 
such a way as to illustrate the fundamental rules for 



ARITHMETIC 363 

multiplication and division of fractions. A pupil can 
learn to divide a line into parts more easily than he can 
master definitions, and when this is done he has a con- 
ception of fractions which he cannot gain in any other 
way." {Report of the Committee of Ten.) 

''It is essential in the first place to make it clear to 
the pupil that a fraction is the result of division into 
equal parts. It is convenient to employ the units already 
introduced, fractions of which can be expressed in terms 
of a smaller unit by means of whole numbers. For 
example, the foot gives halves, thirds, fourths, sixths, 
twelfths as so many inches; the hour (clock face) gives 
in addition fifths, fifteenths, twentieths, thirtieths, six- 
tieths, as so many minutes." {Scotch Memorandum.) 
From such concrete illustrations the pupil will get a 
grasp of the fraction and can easily pass to the symbol. 

These suggestions supplement the advice in New 
York City: " Halves and fourths, thirds and sixths of 
single objects; paper folded into two equal parts, into 
four equal parts, into three equal parts, and into six 
equal parts; objects cut into two, into four, into three, 
and into six equal parts, and one or more of them named. 
The same should be illustrated by drawings." 

Thus pupils have three ways of getting hold of the 
concept of fractions: the concrete objects divided into 
parts, the written words half, fourth, third, sixth, etc., 
and the symbols J, ^, I, i, J, etc. 

711. Principles or laws of fractions. — There are 
three principles to be made clear in fractions. The 
teacher observes them at all times but pupils may know 
many of the processes before the rules are comprehended. 
These are the principles: 

1. Multiplying or dividing both numerator and de- 



364 METHODS IN EDUCATION 

nominator of a fraction by the same number does not 
change the value of the fraction. 

2. Multiplying the numerator or dividing the denom- 
inator of a fraction by a number multiplies the fraction 
by that number. 

3. Dividing the numerator or multiplying the denom- 
inator of a fraction by a number divides the fraction 
by that number. 

These important principles may be developed and 
illustrated by these graphical means: J ft. (6 in.) = f ft. 
{i.e., 2X3 in.) = f ft. (i.e., 3X2 in.) = A ft. {i.e., 
6 in.). This gives the first principle. For the 
second: | ft. = 6 times yV ft. {i.e., 1 in.). Similarly 
for third principle. 

712. Three conceptions of fractions. — Under a strict 
interpretation of number as measurement, the third 
conception embodies the first and the second, but the 
three classes are mentioned for the purpose of discussing 
what is set forth in the different text-books on arith- 
metic. 

1. A fraction is one or more of the equal parts of a 
unit. This is the historic definition and the one still 
used in many books. 

2. A fraction is indicated division. This is some- 
times spoken of as the ratio of a quantity to another 
of the same kind, f means 3-^-4. This means that 4, 
the divisor, is a unit of measure in terms of which 3 
is to be expressed. 6 -^- 2 means that if 2 is the unit, 
what is 6? So also 3^4 means that if 4 is the unit, 
what is 3? The answer is that if 4 is the unit, 3 is 3 
of four equal parts of 4, and therefore f according to 
the first definition. So the second conception passes 
over into the first. 



ARITHMETIC 365 

3. A fraction is an expression of measured quantity, 
ratio. In the process of number we start with a whole; 
we have a unit of measurement; we repeat the unit of 
measurement to make up the whole. In a measured 
quantity represented by a fraction we do exactly the 
same thing. (Psychology of Number, page 138.) In the 
mental process of measurement in which the unit of 
measure is itself defined or measured, there must be 
(1^ a standard unit of reference (the primary unit), 

(2) a derived unit (the unit of direct measurement), and 

(3) the number of these in the quantity. The fraction 
gives complete expression to this process: In $J, for 
example, (1) the dollar is the unit of reference; (2) it 
is divided into four parts to get the derived unit --- the 
actual unit of measure; (3) the '^ numerator" 3 shows 
how many of these units make up the given quantity, 
and expresses the ratio of this quantity to the standard 
unity (page 130). Read pages 124 to 144 in Psychology 
of Number. 

Fundamental Processes in Common Fractions 

713. Changing to equivalent fractions. — This de- 
pends upon the multiplying mentioned in the first 
principle. The approach is made during the first steps in 
halves, fourths, sixths, etc., by noting equivalents, thus: 

1 — 2 — 3 

2 — 4 — 'S 

1 — 2 

3 — ^ 

2 — 4 

3 ~" e 

Then follow simple exercises which prepare for suc- 
ceeding processes. 

3 — ^ 7 ~ T4 

2 3 

3^ — TIT T — IFS 

1 5 

6 — Tn 8 iir 



366 METHODS IN EDUCATION 

Change J to eighths, f to ninths, f to twelfths, | to 
eighteenths. 

714. Reduction to lowest terms. — Apply division of 
terms in principle one to |, f, t\, A, S, It, ht 

715. Whole or mixed numbers. — Changing to whole 
or mixed numbers is the simple process of division; as, 

3 6 8 1_2. _2 4 
Tj Tj 3> 5 , T- 

716. Addition. — Recall that only like numbers can 
be added. 2 bu. + 8 bu. = 10 bu. To add | and |, 
change so that pupils will see 4 eights + 6 eights = 10 
eights. Thus f + I = V-. Addition is well presented 
in most of the text-books. For further exercises, con- 
sult any approved text. 

717. Subtraction. — No new operations or principles 
here. Apply common denominator again. 

718. Multiplication : fraction by integer. — This oper- 
ation appears easy. Take multiplication of fraction by 
whole number first. Proceed as follows: 

$7X5= $35. 
7 dollars X 5 = 35 dollars 
7 tenths X 8 = 56 tenths 

- ^^ 
tenths 

To X 8 = yo 

Explanation by Bailey 

This abstract is taken from an address by L. H. 
Bailey, New York Training School for Teachers, h} 
N. E. A. Report for 1905, page 383. 

*' Let us illustrate by teaching the multiplication of a 
fraction by an integer. Preparation consists of making 
sure that the learner has in mind the knowledge through 
which the discovery of the general principle is to be 



ARITHMETIC 367 

made. What does 8 denote? What does the denom- 
inator denote? What does the numerator denote? 
Presentation consists in selecting an example and in 
finding a method of performing the operation. This 
may be done objectively or abstractly. We will choose 
the former. Let us take f X 2. We will draw a circle, 
separate it into eight equal parts, and shade three of 
them to represent f . Multiplying f by 2 we obtain six 
of these parts, or |. To multiply | by 2, we multiply 
the numerator. Comparison consists in showing that 
every other example in the multiplication of a fraction 
by an integer is exactly similar to f X 2 in all respects 
essential to the demonstration. This is true because 
multiplying the numerator of every fraction by an 
integer will multiply the number of equal parts that 
are taken without affecting the size of the parts. Gen- 
eralization consists in stating the general principle. To 
multiply a fraction by an integer, multiply the numer- 
ator. Application consists in following this general 
principle in the solution of individual examples. Mul- 
tiply T3 by 9. /s X 9 is an example in the multiplica- 
tion of a fraction by an integer; to multiply a fraction 
by an integer, multiply the numerator; to multiply ts 
by 9, multiply the numerator." 

719. Multiplication : fraction by fraction. — The next 
work is to multiply a fraction by a fraction. Develop- 
ment may be as follows: 



'^Xi= ? 
)f X 1 = Si 



'4 /\ J- "«^4 

S3 01 4 = S4 

2 X } = $1 or $i ans. 
In the second step we have used 1 as a multipher 
(process understood from last paragraph). With a mul- 



368 METHODS IN EDUCATION 

tiplier | as large, the product is, J of $f or $J. Using 
f instead of J as multiplier, the product is twice as 
large; hence, 2 times $i or $|. The same result may 
be secured in a shorter process by multiplying the 
numerators for a new numerator and the denominators 
for a new denominator. 

Continued multiphcation is a larger appHcation. Use 
cancellation to review divisors, and reduction to lower 
terms. Emphasize cancellation as a short, practical 

process. ^v/ i5\/ 9 v 35 — 9 

^ /\ 44 /\ To /\ T 8 — • 

Note. — Concerning multiplication of a fraction by a fraction 
it might be pointed out that strictly speaking the expression 
involves contradiction of terms. Multiplication means manifold- 
ing or repeating. The multiplier specifies the number of times. 
But when the multiplier is a fraction, the number of times is not 
all of one time, but only part of a time, and the idea of repetition 
vanishes. I X f, read | times f, strictly speaking, therefore, is 
nonsense and it means and can only mean ^ of f . But inasmuch as 
it is convenient to speak of the process as multiplication and inas- 
much as in any case the world will continue to speak of it as 
multiplication, this is the point at which a somewhat broader 
definition of multiplication should be introduced; namely, finding 
a number that is related to the multiplicand as the multiplier is 
related to unity. 

Graphic Illustration of Multiplication 

f X f Let rectangle AB represent 1. Then 

A I \ — AC will represent f . Then, dividing alti- 
tude into fourths, and drawing lines 
through points of division parallel to 
base, the whole unit A B will be divided 
'^ ^into 20 equal parts and A D, which is f 
of f , is 2% of the whole unit. 

The rule for multiplication may now be made by 



— 


— 




D 


— 











ARITHMETIC 369 

inspecting the terms" of product and factors and noticing 
their relation to each other. Then verification and 
application complete the work. This inductive pro- 
cedure does not answer the question, Why should the 
numerator of the product be the product of the numer- 
ators of the factors? But the inductive method 
never does answer that question (see section 697) 
and insistence on the question why, with reference to 
such rules, means insistence that arithmetic must be 
made a deductive science throughout. 

720. Faulty arrangement. 

Find cost of 3J yards at $2J a yard. 

This statement of the operation does not give mathe- 
matical truth. It says $2J = $8J. Economy of time 
and brevity of form are not advantages here. Arrange 
the work in steps. 

3 J yards = -3^- yards 

$5. \/ 1 — ©50 — <COl 



ans. 



721. Division: fraction by integer. — Recall the third 
principle in section 711 and apply it. 

$18 ^ 3 = $6 
18 dollars -^ 3 = 6 dollars 
18 twentieths -r- 3 = 6 twentieths 
i^ — ^ = -A^ 

When the numerator is not exactly divisible, the de- 
nominator must be multiplied by the divisor. This is 
one process that is mastered long before the reasons are 
understood. Take this: If 4 pads cost $f, what is the 
cost of one pad? Here the process must be by mul- 



370 METHODS IN EDUCATION 

tiplication of denominator, and the answer is $/o or 
15 cents. 

722. Division : fraction by a fraction. — This is an- 
other instance of learning the process before understand- 
ing the reasons for the rule. 

1-1-2. — ? 
8 • 3 ~ • 

1-T- A= 3 
i of 3 = f 

1 „f 3 — 2 1 
8 01 2 — Tff 

Required to divide | by §. Taking the unit 1 instead 
of I, we find that J is contained 3 times in 1. Then f 
is contained in 1 one-half of 3 times or |. As | is only 
I of 1, the true quotient is J of | or H. We see that a 
shorter process to this same result is to invert the terms 
of the divisor and multiply. 

8 A 2 — IB^ 

Inversion of Terms 

Another explanation of inversion of terms in division of 
fractions. 

1 -i- 2 — O 
8 • 3 • 

7 
8 



Or, 



-i- 


2 


= tV 


X 


tV 


= f^ ans. 


X 


3 

2 


= U ans. 



We used 2 as the divisor instead of f , and the quotient 
is tV- But the divisor 2 is 3 times too large; hence, 
the quotient tV is 3 times too small. Then to obtain 
true quotient, we must take 3 times yV- The same 
answer could be secured by the shorter process of inver- 
sion and multiplication. 



ARITHMETIC 371 



Graphic Illustration of Division 

3 _:_ 3 

4 • ^ 

The problem, like every problem in division, is a 
problem in measurement (see a preceding paragraph on 
division of integral numbers) ; the divisor is the unit 
of measure, the dividend is to be measured. The prob- 
lem then means: if f is the unit, what is f? 

, Divide base of unit rectangle into fifths and altitude 
into fourths and draw lines parallel ^ 
to altitude and base respectively. 
The rectangle is thereby divided into 
equal rectangles of which f or AC, 
the measuring unit, contains 12; and 



D 



I or AD, the quantity to be meas- 
ured, contains 15. f -^ f = AD -r- AC = 15 
= |. Therefore f ^ f = if . 

Inductive method. Noting now relation of terms of 
quotient to that of dividend and that of divisor, we 
infer the usual rule. 

Another deductive method. Divide f by f. Let 
X = quotient. 

Statement 1. Then f X a; = |. 

Reason 1. Division is process of finding one factor 
when product and other factor are given. Dividend is 
product, f and x the factors. 

Statement 2. Therefore ^ oi x = J of f. 

Reason 2. If equals are divided by equals, the quo- 
tients are equal. 

Statement 3. Therefore x = 3 X J of f = | of f . 

Reason 3. If equals are multiphed by equals, etc. 

Conclusion, t ^ f = f X f . 

The rule for the inversion of the divisor is here shown 



372 METHODS IN EDUCATION 

to be a necessary logical consequence of the definition 
of multiplication and certain fundamental assumptions 
or axioms. 

723. Equation introduced. — The mooted question 
about the introduction of the equation and x has one 
decisive answer here. The five axioms of equality, 
addition, etc., should be illustrated by lines or the 
balance and the child convinced of their truth. 

724. Division : integer by fraction. — Another case is 
to divide a whole number by a fraction. This case is 
usually treated before dividing a fraction by a fraction. 
But after using inversion, we have a simple procedure : 

7^ f =? 
1- 1= ? 
Here the use of the denominator 1 gives a case exactly 
hke 722. 

Decimal Fractions 

725. Relation to common fractions. — The relation of 
decimal fractions to common fractions is treated under 
three views. 

1. The first opinion favors the teaching of decimal 
fractions as an extension of the decimal system of United 
States money and the decimal systems of money, weights, 
and measures in certain foreign countries. 

2. The second view makes decimal fractions the 
equivalents of certain types of common fractions. This 
means, then, simply another kind of notation, and for 
this reason many text-books treat common fractions 
and decimal fractions together. 

3. The third view considers decimal fractions very 
difficult for a child to comprehend on account of so many 
large denominators. For this reason the subject is 



ARITHMETIC 373 

treated in a separate chapter after common fractions 
have been mastered. 

We need not try to decide whether decimal fractions 
should be taught before common fractions, simultane- 
ously with them, or after them. The vital point is clear- 
ness in presentation; and a satisfactory way seems to 
be to unite the first two opinions and proceed from the 
known decimal scale of United States money and the 
known types in common fractions such as tV, A, to, iho, 

2 3 1 2 + 

T^^, TO'O'jTo o""Oj TooOj etc. 

726. Suggestions for early lessons. — Denominator 
means indicator of denomination; e.g., f, 7 in., 5 hr., etc. 
In the number 358, the 3 and the 5 need no expressed 
denominator because of a convention that everybody 
understands that when digits stand side by side those 
at the left shall have a value dependent upon position. 

Our system being a decimal system, the fractions 
capable of being brought under the system and expressed 
without denominator are the various orders of decimal 
fractions; i.e., those whose denominators are 10 or 
powers of 10. 

As a matter of fact, the extension of our Hindu nota- 
tion to express fractions, or the discovery of decimal 
fractions, is a modern European contribution to the 
system. — Smith, page 6Q. 

It is difficult to see why in such a number as 453.75, 
0.05 is any harder to understand than 400. Denomina- 
tion has to be inferred from position in the one case as 
the other. 0.05 means five of the hundred parts of the 
unit, 400 means 4 groups of a hundred units. 

727. The decimal point. — The one new feature of 
decimals is the decimal point. Pupils know numerator, 
denominator, terms of fraction, value of fraction, frac- 



374 METHODS IN EDUCATION 

tional unit, and the four operations. The use of the 
decimal point need not be entirely new in decimals. 
During the third year of school pupils write such amounts 
as $2.60, $18.74, and others. They add and subtract 
such amounts, putting the decimal points under each 
other. They learn the name decimal point, but they 
do not know the laws of decimals. An authority on 
this is Handbook to SmWs Arithmetics, page 33 (Ginn). 
The specific use of the decimal point in decimals is 
estabhshed by changing to, t\; A, etc., to equivalent 
decimals. The application to hundredths, thousandths, 
and other orders will follow, of course, to bring out the 
principles of decimal fractions. 

728. Principles. 

1. Moving the decimal point one place to the right 
increases the value tenfold; moving two places to the 
right increases the value one hundredfold, etc. 

0.082 

0.82 = 10 X 0.082 

8.2 = 100 X 0.082 

2. Moving the decimal point one place to the left 
decreases the value tenfold; two places, one hundred- 
fold, etc. 

0.882 
.0882 = 0.882 -^ 10 
.00882 = 0.882 ^ 100 

3. Ciphers annexed or rejected at the right of a deci- 
mal do not change the value of the decimal. 

.88 = .880 

729. Development lesson: notation and numeration. 
— The matter for. lessons on decimals may be found in 
any good text. The scope of such lessons is indicated 
here to aid those who need such suggestions. 



ARITHMETIC 375 

1. Matter. Examples covering reading or interpreta- 
tion; writing decimals; reading and writing mixed deci- 
mals. Do not use and in reading whole numbers like 
$125; but use and in place of the decimal point. $125.60 
= one hundred twenty-five dollars aiid sixty cents. 

2. Arrangement. 

(a) Add: $18.65 13.46 inches 

12.48 8.92 inches 

6.22 2.15 inches 

(6) $126.18+ $415.92+ $75.86. 

(c) 74.12 ft. +18.7 ft. + .6 ft. 

(d) 270.40+186.90 + 23.04. 

(e) Read: 

T J TO J 

0.6, .16, 

.705, .023, 

6.306, 42.0094, .3678, 
(/) Write in figures: 

Fifteen hundredths. 
• Seven thousandths. 

One hundred eighty ten-thousandths. 

Forty-four and six hundredths. 
(g) Write in words: 

_5_9 6_ _8 IZ ^4 6.3 

lOOOj TTyTTj 10, T^OOU" 

.0024, 0.8, 7.16, 384.681 

3. Rules. Read the decimal as an integer and give 
it the name of its right-hand order. 

To write decimals: Express the numerator in figures, 
and then place the decimal point so that the last right- 
hand figure shall express the denomination of the decimal. 

730. Addition and subtraction. — Write the numbers 
so that the decimal points shall be in the same column, and 
then add or subtract respectively as in whole numbers. 



1 70 

To^o, 


17 0, 
To OOff 




.160, 


.175, 


2.8, 


.003, 


7.05, 


0.23, 



376 METHODS IN EDUCATION 

1. Matter. Five or more examples in common 
fractions and decimals to satisfy inductive process. 

2. Arrangement. 

(a) Multiply i\ by j%\. 

3 \y _8_4 — _2 52 
To /N lOlT — 100^' 

.3 X .84 = .252. 

/7.\ 12 V 7 5_ — 900 
\0) TOS^ /\ Too — 100 0(7' 

.12 X .75 = .0900. 

(c) 3 X 0.4, 3 X .04, 3 X .004. 

(d) 54.6 X .30. (e) 0.24 X .254. 

3. Rule. Multiply as in whole numbers and point 
off as many places in the product as there are decimal 
places in both multiplicand and multiplier. 

4. Observation. The principle that product is re- 
lated to multiplicand as multiplier is related to unity 
has an important bearing on the question of fixing the 
decimal point in product. For example, 423.35 X 0.023 
product is of third order below hundredths because 
multiplier is of third order below unity. 

5. Abbreviated Multiplication. The following 
method is easily explained by reference to foregoing prin- 
ciple, and it is valuable for many reasons. Find to second 
decimal place circumference of circle whose diameter is 
34.62 m. The solution is 34.62 m. X 3.1416 = circum- 
ference. 

Solution. 34.62 Diameter 

6141.3 Ratio C:D. 

103.86 

3.46 

1.38 

.03 

.02 

108.75 Circumference. 



ARITHMETIC 377 

Rule. Write multiplier in reverse order, placing units 
place under that place of multiplicand in which accuracy 
is desired in product. In multiplying by any term of 
multiplier, reject that part of multiplicand lying to the 
right of term of multiplier in use. 

Explanation. Multiply 34.62 by 3 units. Product 
will be hundredths. 

Multiply 34.6 by 1 tenth. Product will be hundredths 
according to principle in No. 4. 

Multiply 34 by 4 hundredths. Product will be hun- 
dredths according to principle in No. 4, etc. 

The method has the advantage of avoiding useless 
work as well as that of doing the most instead of the 
least important part of the work first. It also furnishes 
an automatic arrangement for rejecting so much and 
only so much of multiplier as will not affect product. 
Besides all that, it furnishes an excellent method of 
making pupils give real reasons rather than thumb 
rules for their steps. 

731. Division: related to common fractions. — The 
old way is analogous to the plan used in multiplication; 
namely, from common fractions to equivalent decimal 
fractions. This shows the reason for the rule that the 
quotient contains as many decimal places as the decimal 
places in i\\e dividend exceed the decimal places in the 
divisor. 

732. Division : Austrian method. — In division we 
have also an "Austrian method," a valuable arrange- 
ment. It is not long since a problem like 6.275 divided 
by 2.5 was " worked " by a rule which was rarely devel- 
oped. Now the work is arranged in this way: 



378 METHODS IN EDUCATION 

2.51 

2.5)6.275 25)62.75 

50 

12.75 
12.5 

0.25 
0.25 
Such an arrangement leaves no trouble with the 
decimal point, and the work is easily explained. In the 
above problem the entire remainder is brought down 
and the decimal point is preserved throughout, as should 
be done until the process is thoroughly understood; then 
the abridgment should appear. — Smith, page 122. 
733. Division: inverse of abbreviated multiplication. 
Example. What is the diameter of circle whose cir- 
cumference is 108.75 meters? 

Solution. 3.1416 X Diameter = Circumference 
Diameter = Circumference 

3.1416 
Arrangement as in Austrian method above. Only 
variation from that method is to reject successively one 
place in divisor instead of bringing doAvn one more 
place from dividend in remainder. This rejection would 
mark off 1416. 

34.62 

3.1416)108.75 
94.25 

14.50 
12.57 

1.93 

1.88 



ARITHMETIC 379 



Denominate Numbers 

734. Turn to use. — This part of arithmetic has been 
mentioned several times in illustrating the application 
of concrete or objective methods of teaching. All the 
tables now used are taught by measuring and counting. 
This is one application of the maxim, "Turn to use. " 
Toy money in actual problems makes the way to the 
table of United States money; familiar use of the foot- 
rule and yard-stick leads to the table of linear measure; 
the measurement of desks, boards, floor, and walls shows 
a need for square measure; one more dimension in the 
schoolroom, in boxes, bins, crates, cellars, etc., intro- 
duces cubic measure. Likewise in dry measure, liquid 
measure, and avoirdupois weight. The inference is that 
the tables should be built, constructed, or made according 
to actual uses instead of being memorized first and then 
applied. It is the inductive method instead of the 
deductive method. 

It is at this point, in the use of compound numbers, 
that geometric and physical principles must be made 
use of. The straight line and curved, the rectilineal 
figures and the circle, the right angle and other angles, 
the square, rectangle, the fundamental concepts, and 
principles of solid geometry as well as effects of gravita- 
tion, specific gravity, principles of lever, of flotation, 
and the like are necessary in order to make the use of 
the units of denominate numbers intelligible. These 
are the problems that add interest to arithmetic and give 
it a real content, that make it the subject that deals in a 
concrete, experimental way rather than by the method 
of deductive demonstration. See Committee of Ten on 
Arithmetic and Concrete Geometry, pages 107 and 110. 



380 METHODS IN EDUCATION 

Percentage 

735. Relation to fractions. — Percentage is a direct 
outgrowth of the use of common fractions and decimal 
fractions. When we come to speak of the different 
methods of presenting the work in percentage, fractions 
suggest two of the methods, namely: what is called the 
fractional method or that of common fractions, and the 
decimal method or that of decimal fractions. A third 
method is the algebraic method commonly known as 
the equation. The use of the old formulas for base, 
rate, percentage, amount, and difference is no longer 
sanctioned. 

736. Method of common fractions. — This method is 
a favorite one because (a) it uses the knowledge of 
common fractions; (h) cancellation is employed as a 
short, useful, pleasant process; and (c) there is little to 
distract the child's attention under such a direct process. 

This use of fractions may be arranged according to 
difficulties. 

1. Fractions that cannot be reduced to lower terms; 

_3_ ^7_ _9_ _1_3_ _6_1_ 
lOOj ToOj 10?7j 100; 100- 

2. Fractions that can be reduced to lower terms; as 

^8_ 1_2_ 1_8_ _4 6 
ToOj TOO) TOO) 100' 

3. Complex fractions; as, 

T00> Too? TOO' 100- 

A caution should be observed against the use of large 
numbers in complex fractions. Such fractions are use- 
less if they go beyond the demands of ordinary business 
hfe. 

4. Aliquot parts; as 

16? _ 1 334 = 1 
ITU 6 J TOO 3- 



ARITHMETIC 381 

A chart showing the equivalent ahquot parts should 
hang in every class-room. 



12i 
TOO 


= 


1 
8 


= 


100/0 


.125 


25_ 
Too 


= 


1 
4 


= 


25 % = 


.25 


37i 
Too 


= 


3 

8 


= 


37i% = 


.375 


T%% 


= 


1 
2 


= 


50 % = 


.50 


62i 
TOO 


= 


5 

8 


= 


62J/0 = 


.625 


tVo 


= 


3 

4 


= 


75% = 


.75 


8 7* 
To5 


= 


7 
8 


= 


87i% = 


.875 


1 en 
Too 


= 


1 
6 


= 


161% = 


.16! 


33J 
100 


= 


1 
3 


= 


33|/o ~ 


.331 


66§ 
TOO 


= 


2 
3 


= 


661% = 


.661 


83^ 
TOO 


= 


5 
6 


= 


83§% = 


.83J 


20_ 

TOO 


= 


1 
5 


= 


20% = 


.20 


_4 0_ 
100 


= 


2 
5 


= 


40% = 


.40 


T%% 


= 


f 


= 


60% = 


.60 


l%% 


= 


4 
5 


= 


80% = 


.80 



Other ahquot parts may be used and other arrange- 
ments on the chart may be preferred. The given plan 
emphasizes the grouping of the aliquot parts as common 
fractions in their simplest form as given in the second 
column. Pupils should memorize this chart. 

737. Method of decimal fractions. — The table of 
ahquot parts may be used as a table of equivalents also. 
Then the apphcations of decimal fractions in percentage 
are matters of substituting the equivalent decimal for 
the common fraction. The interpretation of the prob- 
lem brings nothing new; the operation itself is the same; 
and the regular principles of decimals are adequate. 

738. The method of the equation. 

1. This is a vahd use of algebra to simphfy relations 
and processes in arithmetic. The early work in arith- 



382 METHODS IN EDUCATION 

metic has made pupils familiar with such examples as 
these: 

6 X ? = 48? 

7 X ? = 63? 
11 X $? = S132? 

2. The next step is to see that pupils understand that 
per cent means hundredths, hundredth, or of a hundredth; 
as 

6 per cent means 6 hundredths. 

1 per cent means 1 hundredth. 

I per cent means | of a hundredth. 

3. The third step in teaching the equation is to im- 
press again the meaning of the symbols yf o, .06, and 
6%. The table of equivalents should show that all 
three forms mean the same. 

4. A fourth step is a review of the decimal method in 
percentage. These preparatory steps are really a review 
of all the work in percentage. Then the pupils are 
ready for the equation. 

6x?= 30? 

6 times what number = 30 ? 

Qx = 30. By algebra. 

If Qx = 30, what is the value of x? 

If ^x = 30, what is the value of re? 

If Jx = 30, what is the value of x? 

If j^x = 30, what is the value of x? 

If .5a; = 30, what is the value of x? 

If 0.05x = 30, what is the value of x? 

If 0.005a; = 30, what is the value of x? 

5. Application. 

$12 is 4% of how many dollars? 
$13 is 4^% of how many dollars? 
20 miles is 5% of how many miles? 



ARITHMETIC 383 

6. Form. 

0.04a: = $12 
0.04ir = $13 
0.05a; = 20 miles. 

7. An example solved. // an automobile is sold for 
$1025 at a profit of 25%, how much did it cost? 

Let X = cost 
.25a: or \x = gain 
X + .25a; = $1025, selling price. 
1.25a; = $1025 
X = $820, cost. 

Siriiple Interest 

739. Terms used. 

1. The sum of money on which interest is paid is the 
principal. 

2. The per cent, of the principal paid for the use of 
the principal for one year is the rate. 

3. The money paid for the use of the principal for 
the entire time is the interest. 

4. The interest added to the principal is the amount. 

740. Methods. 

1. When the time is an exact number of years and 
months, find interest for one year and multiply this by 
the number of years. 

2. Six per cent method. 

3. Exact interest is interest obtained by considering 
365 days as one year. 

741. Faulty Arrangement. 

Avoid untrue statements like the following solution 
in finding the interest on $500 for four years at 
T^oo X $500 = $30 X 4 = $120. 



384 METHODS IN EDUCATION 

Arrange the work in two steps. 
$500 X xf = $30 
$30 X 4 = $120 ans. 

Miscellaneous Topics 

742. Algebra used in arithmetic. — The close relation 
between arithmetic and algebra is no longer a matter 
of doubt. Nearly all the modern text-books on arith- 
metic have introduced the elements of algebra. The 
rule and its hmitations may be stated thus: Use algebra 
wherever its use will make the processes in arithmetic 
easier or clearer. 

743. Ratio. — Relation in arithmetic is ratio. In- 
stead of waiting to reach this topic in the last part of 
arithmetic, it is advisable to use it all through arith- 
metic. Every analysis that directs attention to com- 
parative quantity uses ratio. Hence, the importance 
attached to unitary analysis, variable unit, common 
fractions, and equations. 

744. Short processes and business methods. — Mod- 
ern usage favors the introduction of short processes 
whenever they are of such a nature that the child can 
readily comprehend their practical value. For instance, 
in multiplying by 10 or any multiple of 10 the addition 
of the number of ciphers found in the multipher is a 
direct way to the product; in dividing by 10 or any 
multiple of 10 pointing off to the left as many places as 
there are ciphers in the divisor; cancellation, factoring 
by inspection, the use of aliquot parts in common frac- 
tions and percentage and the contracted methods in 
interest and the other applications of percentage. Dr. 
Smith says that the teacher who fails to keep in touch 
with the demands and methods of modern business is not 



ARITHMETIC 385 

doing her duty toward herself or the class. In regard to 
business methods considerable discussion has arisen about 
how much commercial arithmetic should be introduced in 
the regular courses. This question brings in the phases of 
commercial discussion which cannot be treated fully here 
but suffice it to say that the text-book in use in the school 
may serve as a guide in the limitations in this matter. 

The following footnote, page 218 of the Young's The 
Tsacliing of Mathematics, is a good presentation of 
the demands of business. 

" An excellent idea of what the business world believes 
it has the right to expect from schools is given in Still's 
report to the N. E. A. 1900, digested from six hundred 
replies representing fifty-seven different occupations and 
lines of business. 

*' Mechanical Aids: — 

1. Importance of decimal point in business. 

2. Necessity for legible figures. 

3. Accuracy and speed. 

4. Use of interest and discount tables and graded 
schedules. 

5. Use of cash registers and arithmometers. 

6. Fractions hke f , it, il, etc., should receive scant 
attention. 

7. Importance of ''short cuts." 

8. Value of teaching multiplication table through 
20 X 20. 

9. Importance of familiarity with English money. 

10. Business forms, such as checks, notes, receipts, 
statements, and price lists should be understood by all 
pupils of the seventh year and upward. 

11. Constant repetition and drill in the use of the 
four fundamental processes. 



386 METHODS IN EDUCATION 

12. Processes of Solution. (In reply to question as 
to differences between processes of school work and 
outside world.) On the whole, no great differences. 
(In interest, the only case, find interest and amount: 
facility in the four fundamental processes and approx- 
imate estimates important.) " 

745. Unitary analysis. — This kind of analysis goes 
back to one common unit of measure. The fixed unit 
one is the basis. 

Illustration. Six books cost S9; find cost of eleven 
books at the same rate. 

$9 = cost of 6 books 
$9-^6= Hi, cost of one book. 
Hi X 11 = $16.50, cost of 11 books. 
The other important method of solving problems is 
the equation. 

746. Variable unit. — In contrast to the fixed unit 
one, we have the variable unit. When a convenient 
ratio exists between the two quantities in the problem, 
it is convenient to use that ratio instead of going back 
to the cost of one. 

Illustration. Six books cost $9; find cost of thirty- 
six books. 

$9 = cost of 6 books. 
Ratio of 6 books to 36 books is 6. 
Hence, $54 = cost of 36 books. 
The unit of comparison happens to be 6, but it might 
be any other number. Note that this device does not 
apply to the problem in 745; there is no integral ratio 
between 6 and 11. 

747. Series. — Grube and others have used the series 
of combinations for abstract and concrete drill. Illus- 
tration of series in building number 7: 



ARITHMETIC 387 

6+1=7 1+6=7 2+2+2+1=7 

5+2=7 2+5=7 3+3+1=7 

4+3=7 3+4=7 

748. Arithmetical complement. — The difference be- 
tween any number and the next higher power of 10 is 
the arithmetical complement of that number. 

3 is the complement of 7, since 7 + 3 = 10. 
32 is the complement of 68, since 68 + 32 = 100. 
135 is the complement of 865, since 865 + 135 = 1000. 
0.26 is the complement of 0.74, since 0.74 + 0.26 = 1. 

749. Problems. — " Problems include all the examples 
in arithmetic in which the operations are not directly 
stated. They are divided into simple, involving only 
one operation, and complex, involving more than one 
operation. The solution of these problems is always 
made through a form of reasoning called traduction." 

750. Proof, verification, or checking. — The proof of 
correct solution may be answers in the book, the teacher's 
decision, a second solution in the same way or in another 
way. Verification of a few problems is worth more than 
the solution of many additional problems without veri- 
fication or proof. Some kinds of proof have been men- 
tioned. Here we add that of casting out 9's. This is 
useful but it fails to detect such errors as the addition 
of 9, the interchange of digits, and all errors not affecting 
the sum of the digits. 

Casting out 9's to Check Addition 

751. Rule. — The excess of any number over a mul- 
tiple of 9 is equal to the excess of the sum of its digits 
over a multiple of 9. 

745 = 9(82) + 7 Excess 7. 

7+4+5=9X1+7 Excess 7. 



388 METHODS IN EDUCATION 

The proof is practically identical with that given for 
test of divisibility by 3. 

a+ 6+ c-\- d-{- e = sum of digits, 

a + 10 6 + 100 c + 1000 d + etc .= the number. 

9 6+ 99 c + 999 d + etc.=^ multiple of 9. 
a+ 6+ c+ d-\- etc. by subtracting. 

This signifies that a number is equal to the sum of its 
digits plus a multiple of 9. Hence throw out all the 9's 
from the sum of the digits and the remainder is the same 
as though the 9's were thrown out from the number 
itself. Now take the several examples, throw out the 
9's from the sum of the digits, and according to the rule 
we infer that 

56342 = a multiple of 9+2. 

64723 = another multiple of 9+4. 
57849 = a third multiple of 9+6. 
23454= a fourth multiple of 9+0. 

202368 = a fifth multiple of 9 + 12. 

The sum of several multiples of 9 must itself be a mul- 
tiple of 9. If a number is contained in each of several 
numbers it is contained in their sum. If equals are 
added to equals, the sums are equal. 

But a fifth multiple of 9 + 12 = a sixth multiple of 
9 + 3, and we perceive (casting out 9's from sum of 
digits) that 202368 = a multiple of 9+3. But it is 
impossible that the same number shall at same time be 
equal to two different multiples of 9+3. Therefore 
the work is probably correct. 

Text- Books in Arithmetic 

752. Guiding principles. — Arithmetic is no excep- 
tion to the two pedagogical principles governing the 



ARITHMETIC 389 

selection and use of subject-matter. The sociological 
principle requires matter to be such as will appeal to 
present and future interests of the community; and 
the psychological principle requires adaptation to the 
spiritual capacities. The former determines the nature 
of the problems; the latter decides arrangement of book 
and method of teaching. 

753. Elimination of subject-matter. — The modern 
text-books are leaving out a large number of the topics 
treated in the older books. This view is looking to the 
practical value of what is learned in mathematics rather 
than to the disciplinary value of the study. Young 
argues for simphfication and suggests, on page 220, the 
elimination of the following: 

1. G. C. D. or L. C. M. of large numbers otherwise 
than by factoring. 

2. Fractions with large or unusual denominators. 

3. Compound or complex fractions. 

4. All measures not actually in use in the community 
at large. 

5. Reductions of decimals to common fractions and 
decimals beyond thousandths. 

6. Circulating decimals. 

7. Square root and cube root except by factoring. 

8. Profit and loss as a separate subject. 

9. True discount. 

10. Partial payments. 

11. Equation of payments. 

12. Partnership. 

13. Compound proportion. 

14. Compound interest. 

15. Business forms which do not conform to the usage 
of the day. 



390 METHODS IN EDUCATION 

16. Large numbers and exercises involving many 
numbers. 

17. The premature introduction of difficult matter. 

754. Content of the problems. — The elimination of 
matter implies a very close observance of child psychol- 
ogy and business demands. What, then, should be the 
bearing or nature of the problems? The answer is that 
the problems should conform to the spirit and content 
of American life. It is argued that the content taken 
from geography, history, science, and industrial life is 
likely to divert attention from the process, but this 
argument falsely assumes that the teacher is only a 
passive agent. Such content is a basis for interest that 
readily permits transition to drill that assures mastery 
of the processes. '' Every usable arithmetic has always 
been an encyclopedia," says Smith; ''what we have to 
determine is whether it shall now be an encyclopedia 
of vital, modern facts, or one of obsolete, dull, useless 
information." (Monograph, 1909, page 16.) 

Young takes a similar view as he discusses the source 
of problems in the quantitative side of nature, pages 
209 to 214. 

Compare sections 649, 749, and 763. 

755. Types of books. — The arrangement of material 
is the second characteristic of modern books, the first 
characteristic being the nature of the problems. The 
old books treated each topic exhaustively, and the com- 
pletion of the book implied the mastery of the subject. 
The other extreme is a different book for every grade, 
the eight books constituting an elementary series. Be- 
tween these extremes, we find several three-book series. 
The lack of uniformity in grading and courses of study 
does not encourage the effort to produce one series of 
arithmetics to satisfy American schools. 



ARITHMETIC 391 

Three types of books may be mentioned. 

1. Topical. This arrangement is the old type modi- 
fied by ehmination or other means of adjustment. In 
presenting a complete treatment of common fractions, 
for instance, the teacher can use her judgment about the 
quantity of material to be used, the order, the assign- 
ment to groups, the drill, etc. The ambitious pupils 
can go on by themselves, irrespective of class or grade 
limitations, because they and the teacher feel the stimu- 
lus of definite, unified, and complete presentation of the 
work. The topical arrangement is a compliment to the 
tactful judgment of the teacher and a source of joyous, 
invigorating responsibility to the child. 

2. Concessive or Adapted. This type of book em- 
bodies the best according to writers of books, and at 
the same time arranges the matter to suit the average 
demands of several leading courses of study. It is 
eclectic in trying to choose desirable material, con- 
cessive in trying to suit those who make courses of 
study, praiseworthy in trying to bring about uni- 
formity, and hopeful in contributing to an American 
ideal. It may be largely topical, largely spiral, or 
sanely composite. 

3. Spiral. This type is the extreme reaction against 
the old topical books. It is based upon that view of 
psychology which figuratively uses concentric circles to 
represent the child's thought from year to year. ''It 
consists," says Smith on page 119, ''in taking the class 
around a circle, say with the topics of common fractions, 
decimal fractions, greatest common divisor, and square 
root; then swinging around again on a broader spiral, 
taking the same topics, but with more difficult problems; 
then again, and so on until the subjects are sufficiently 



392 METHODS IN EDUCATION 

mastered." But it is a mistake to assume that the nor- 
mal child's progress can be arbitrarily limited in that 
way. The same mistake is observed in the Grube 
method. There is a deadening effect on the pupils on 
account of the fragmentary treatment, rigid gradation, 
and the inhibition of initiative that would otherwise 
take certain pupils far ahead of their less industrious 
companions. It is encouraging to know that this type 
of book is passing into the second type. 

New York City Point of View 

756. Suggestions. — The sections 757 to 766 inclusive 
are from the Course of Study, and the subsequent sec- 
tions are based upon the course of study. While this 
information is helpful for all students, it is used here 
especially for those who are required to know it. 

757. General directions. 

1. Much oral drill and blackboard work should be 
given. 

2. Answers should be tested approximately to ascer- 
tain whether they are probably correct. 

3. The results of addition, subtraction, multiplica- 
tion, and division should be proved before they are 
declared. 

4. Excessive repetitions of forms of analysis and elab- 
orate written explanations should not be required. 

5. Definitions should not be required until the mean- 
ings of the terms to be defined are fully understood. 

758. The combinations. — Special importance is at- 
tached to the thorough mastery of the combinations in 
addition, subtraction, multiplication, and division. The 
following are the steps which should be followed in 
learning the combinations of each table: 



ARITHMETIC 393 

759. Addition and multiplication. 

1. Care should be taken that the pupils apprehend 
the nature of the required operations. 

2. The combinations that have been taught in the 
preceding grade should be reviewed frequently. 

3. The results of the new combinations should be 
determined in addition by counting objects, and in 
multiplication by adding the multiplicand as many 
timgs as there are units in the multiplier. 

4. The entire table should be repeated with the 
objects in view in addition, and with the addends in 
view in multiplication. 

5. The entire table should be repeated without the 
objects or addends in view. 

6. The results of combinations, miscellaneously pre- 
sented, should be given without the aid of any form of 
mnemonics or external devices. If a pupil misses a 
combination, there are two methods of correction: in 
addition he may be told to count objects, and in mul- 
tiplication to add numbers; or he may be required to 
deduce the result of the combination in question from 
the nearest combination whose result he knows. (Thus 
he may ascertain that 6 X 7 = 42 from 5 X 7 = 35, 
since 6 sevens are one seven more than 5 sevens.) The 
former method is objectionable for two reasons: the 
performance of an isolated example will be of little 
value to aid association the next time the combination 
occurs; and the pupil is in danger of forming the habit 
of using his fingers as counters. The value of the refer- 
ence to the nearest known combination consists in the 
association of the combination in its proper relations 
with the other terms of a series. 

7. Exercises in finding the parts which constitute a 



394 METHODS IN EDUCATION 

number either as addends or as factors should follow 
the drills on tables. 

8. The combinations should be applied in the solu- 
tion of simple problems. 

760. Subtraction and division. 

1. Each combination in subtraction and in division 
should be related to its corresponding combination in 
addition or in multiplication. In subtraction the minu- 
end is the sum and the subtrahend is one of the terms 
of a combination in addition; in division the dividend is 
the product and the divisor is one of the terms of a 
combination in multiplication. 

2. The results should be stated without the relation, 
in order that they may be given instantly. An error 
should be corrected by reference to the primary com- 
bination. 

3. The combinations should be applied in the solu- 
tion of simple problems, in order that their mastery may 
be seen to be a means to an end. 

761. Constructive and inventional exercises. — Aside 
from the consideration of their educational value, the 
constructive and inventional exercises of the seventh 
year have been selected with a twofold purpose in 
view : 

1. To furnish pupils with a knowledge of the essential 
elementary principles involved in the work in mensura- 
tion in grade 8A. 

2, To furnish pupils with a knowledge of the con- 
structive principles employed in mechanical drawing 
and construction and in shop work. 

The method of teaching these exercises should be 
suggestive in form and spirit. Formal demonstrations 
should never be required. 



ARITHMETIC 395 

762. Problems. — Numerical relations may be found 
wherever the mind seeks them; hence problems may be 
derived and should be derived from the life of the home, 
the school, the farm, the laboratory, the factory, and 
the railroad, as well as from the shop and the bank. The 
limitation of problems to transactions in dollars and 
cents tends to give practical arithmetic a purely formal 
and disciplinary character; on the other hand, excursions 
inta other fields of human activity, while sacrificing 
nothing of the disciplinary value of the subject, give it 
a varied and interesting content. Problems may be 
classified as simple, or those involving only one opera- 
tion, and as complex, or those involving more than one 
operation. 

763. What to look for in the solution of problems. — 
The solution of problems should be effected by the dis- 
covery of what is given, what is required, and what is the 
relation between these terms. If difficulty is experi- 
enced in the determination of the relations between large 
numbers, small numbers should be substituted. 

764. Analysis in solution. — A brief and well expressed 
form of analysis should be employed in the solution of 
problems to find a part of a number, to find a number 
when a part is given, to find what part one number is of 
another, and to find a number when the number plus 
or minus a part is given, whether common fractions, 
decimals, or per cent expressions are involved. 

765. Rote work criticised. — The mere manipulation 
of numbers in a set order, which the pupils accept on 
authority as the means to a correct answer without 
comprehending the reason therefor, is a form of rote 
work that ought not to be tolerated except in the teach- 
ing of involved and difficult processes to young children 



396 METHODS IN EDUCATION 

as, for example, the process of long division, or the Euclid- 
ean process of finding the greatest common divisor. 

766. Progressive advance in difficulties by grades. 
— The following tabulation shows the progressive ad- 
vance in the complexity of problems through the grades: 

lA. — Simple problems solved without formal ex- 
planations. 

The children represent the terms by objects and find 
the results by counting; no term is greater than 10. 
These involve: 

1. Addition and subtraction. 

2. Multiplication and division. 

IB and 2 A. — Simple problems solved without formal 
explanations. 

The children apply the combinations in addition and 
subtraction as soon as they have mastered them; no 
term greater than 20. These involve: 

1. Addition and subtraction. 

The problems are similar to those in 1 A, but the results 
are found from a knowledge of the combinations involved. 

2. Multiplication and division. 

The problems are similar to those in lA. 

Problems in multiplication are solved by writing the 
multiplicand as many times as there are units in the 
multipher, and by adding. 

Problems in division are solved as in lA by counting. 

2B and 3A. — Simple problems solved without formal 
explanations. 

The children apply the combinations in multiplication 
and division as soon as they have mastered them. These 
involve : 

1. Addition and subtraction. 

The problems involve larger terms than in the pre- 



ARITHMETIC 397 

ceding grades, and the results are invariably found by 
aid of the combinations. 

2. Multiplication and division. 

The problems are similar to those in 1 A, but the results 
are found from a knowledge of the combinations involved. 

3B. — Complex problems solved without formal ex- 
planations. These involve: 

1. Finding a fractional part of a number. 

2.» Two operations — relations direct. 

4A. — Complex problems solved by analysis. These 
involve : 

1. Finding a number when a fractional part of it is 
given. 

2. More than one operation — relations direct. The 
problems are similar to those in 3B, but are explained 
formally by analysis. 

4B. — Complex problems solved by analysis. These 
involve : 

1. Finding what fractional part one number is of 
another. 

2. More than one operation — relations indirect. 
5A. — Complex problems solved by analysis. These 

involve : 

1. Finding a fractional part of a number. 

2. Finding a number when a fractional part is given. 

3. Finding what fractional part one number is of 
another. 

4. Other problems usually given under the head of 
common fractions. 

5B. — Complex problems solved by analysis. These 
involve : 

1. Finding a decimal part of a number. 

2. Finding a number when a decimal part is given. 



398 METHODS IN EDUCATION 

3. Finding what decimal part one number is of 
another. 

4. Finding a number when the number plus or minus 
a fractional or a decimal part is given. 

5. Other problems usually given under the head of 
decimals. 

6 A and 6B. — Complex problems solved by analysis. 
These involve in 6A: 

1. Finding a per cent part of a number. 

2. Finding a number when a per cent part is given. 

3. Finding what per cent part one number is of 
another. 

4. Finding a number when the number plus or minus 
a per cent part is given. 

5. The problems usually given under the head of 
denominate numbers. 

These involve in 6B: 

1. The first four subdivisions of 6 A as appHed in 
business. 

Each should be related to the corresponding problem 
in which a common fraction instead of a per cent 
expression is involved. 

7A. — Complex problems solved by analysis. These 
involve : 

1. Simple interest — direct case. 

2. Metric system. 

3. Foreign money. 

4. Longitude and time. 

5. Common relations. 

7B. — Complex problems solved both by analysis and 
by algebra. These involve: 

1. Simple interest — indirect cases. 

2. Simple interest — applications. 



ARITHMETIC 399 

3. Percentage — indirect cases. 

4. Problems solved by proportion. 

5. Common relations. 

8A. — Complex problems solved by analysis or by 
algebra. These involve: 

1. Mensuration. 

2. Business relations. 

3. Common relations easily expressed by two un- 
known quantities. 

767. Problems illustrating progressive order of diffi- 
culties. — This section gives illustrative examples and 
problems that may be used to overcome difficulties in 
the order in which those difficulties arise. 

Suhtradion 

1. 8—5. Inverse of addition. 

2. 14 — 9. Inverse of addition; borrowing. 

3. 24 — 9. Borrowing units. 

4. 213 — 38. Borrowing units and tens. 

5. 304 — 126. Zero and borrowing hundreds. 

Multiplication 

1. 297 X 135. No zero used. 

2. 297 X 130. Zero in the units column. 

3. 297 X 103. Zero in the tens column. 

Division 

1. 786 -^ 265. No zero in divisor. 

2. 786 -^ 205. Zero in tens column, 

3. 780 -V- 250. Zero in units column. 



400 METHODS IN EDUCATION 



1. f + 1 + 
2 



6 2 

7 7 



Addition and Subtraction of Fractions 
Denominators the same. 



-7 n- T 



3. i+f+^ 
4. 

*-'• 8 n^ 3 T^ 5 

7 __ 3 
'8 ^ 



4 18 12 
3 1 

"8 4 



One denominator is common denom- 
inator. 

^ , ^ J Miscellaneous denominators. 

D. 

7. Bought 3| lbs. Ceylon tea, 2f lbs. of Japan tea, 
and 5f lbs. Canton tea. How many lbs. in all? 

8. A merchant bought 28| bu. potatoes. He bought 
7| bu. from A, 13f bu. from B, and the remainder from 
C. How many bu. did C sell? 

9. Fred walked 121 miles, Luke 13i^o miles, and 
Walter 4f miles. How far did the three boys walk? 

Subtraction of Mixed Numbers 

1. 12| — 5f . Same denominators. 

2. 12| — 5f . 8 = common denominator. 

3. 12f — 5|. Same denominators; borrowing. 

4. 12| — 5f. Different denominators; borrowing. 

5. 12^1 "~ 5xT. Denominators difficult. 

Multiplication of Fractions 

1. f of $16. Familiar operation. 

2. f X 12. Fraction by integer. 

3. 12 X f. Integer by fraction. 

4. f X |. Fraction by fraction. 

5. At $f a yard, what is cost of 75 yds.? 

6. Find cost of 10 tons of coal at $6f a ton. 

7. Find cost of f can of molasses at $| a can. 

8. If land is worth $40J an acre, what is the value of 
a farm of 12i acres? 



ARITHMETIC 401 

Division of Fractions 

1. f -i- 3. Numerator divided. 

2. f -i- 3. Denominator multiplied. 

3. 12 ^ I See section 724. 

4 3 _:_ 1 

5. 6J ^ 2. 6. 6i ^ 2i. 

7. A woman exchanged 30 lbs. of butter at $.25 per 
lb. -for cloth costing $.37§ a yard. How many yards 
did she get? 

Division of Decimals 

Addition, subtraction, and multiphcation of decimals 
do not involve many difficulties. Following is an order 
for division: 

1. 638.724 -^ 12. 2. 63872^ .12. 

3. 638.72 ^ .012. 

4. At 5J cents per lb., how much sugar can be bought 
for $4.40? 

768. Methods applied in New York City. — This sug- 
gestive work is more specific than what precedes in the 
chapter on arithmetic. 

Addition 

769. Grade lA. — Combinations of numbers of one 



order with 1 and 2. 














1 


2 


9 




1 


1 


1 




1 


1 


1 to 


1; 


also 


2 


3 


4 


to 


9 


2 


3 


10 




3 


4 


5 




10 



234 9 222 2 

2 2 2 to ^ also 3 4 5 to 9 
456 IT 567 11 



402 METHODS IN EDUCATION 

These combinations are taught by counting objects; 
later the value of each is recognized at sight, without 
counting, and memorized. No written addition in this 
grade. 

770. Grade IB. — New combinations. 

3 4 9 3 3 3 3 

3 3 to _3| also 4 5 6 to _9 

6 7 12^ 7 8 9 12 



4 


5 


6 9 4 


4 


4 4 


4 


4 


4 to 4; also 5 


6 


7 to 9 


8 


9 


10 13 9 


10 


11 13 



Written addition: numbers of one order, numbers of 
two orders, within the tables, with no carrying. Use 
lA combinations at first. 

(1) 



(2) 
(3) 



2 


1 


1 








1 


3 


5 
















1 


2 


1 


3 


1 




2 


2 


2 


1 







1 


1 


1 


1 


5 




1 


1 


11 


12 




11 






11 


10 




12 






11 


12 




11 






11 


10 




12 






11 


11 




11 







When teaching addition of two orders, designate units 
and tens columns. 



ARITHMETIC 403 

Now use examples with IB combinations, no carrying. 
13 43 31 
23 11 11 
3_ 2? 12 

34 
10 

In column addition, not more than five numbers to 
be used, and no addend greater than four to be used. 

In this grade the signs + and = are used in tables. 

771. Grade 2A. — The tables through 9's completed. 
5 6 to 7 5 5 to 5 

5 5 5 6 7 9 



6 


7 to 


9 




6 


6 


6 


6 


6 


6 




7 


8 


9 


7 


8 9 






7 


7 




7 


7 7 






8 


9 




8 


9 




8 








8 


8 




9 








9 














9 















Written addition: numbers of two and three orders; 
in column addition, not more than five addends; addi- 
tion with carrying. 

Numbers of two orders. Here it is necessary to reach 
the fundamental fact that ten units make 1 ten. 
26 34 13 

33 26 7 

1 31 76 



404 METHODS IN EDUCATION \ 

Numbers of three orders; carrying units only. 

231 713 

416 134 j 

138 149 etc. j 

■j 

Numbers of three orders; carrying units and tens. i 

314 347 I 

486 ' 266 ' 

121 143 etc. I 

141 382 624 

463 110 40 

123 235 103 

146 117 71 J 

31 110 76 i 



Teach fact that ten tens make one hundred. 

In the 2B, the column addition is limited to 6 addends. 

772. Grade 3 A. — Numbers of four orders; carrying 
into the thousands column. Special attention given to 
accuracy and rapidity. 

Subtraction 

773. Grade lA. — Subtraction in this grade is taught 
objectively, and as the inverse of addition. 

6+2=8 carries with it 6 +? = 8, and ? + 6 = 8 
or 8 less 6 = ? 8 less 2 = ? 

774. Grade IB. — Subtraction within the tables. 
1-0=1 2-2=0 
1-1=0 3-3 
2-1=1 4-4 to 9-9 
3-1=2 

4-1=3 to 9-1=8 



ARITHMETIC 405 

Minus sign (— ) taught; vertical form taught. 
(1) 1 2 3 to 9 

- 1 - 1 - 1 - 1 



(2) 


15 


26 


36 






- 1 


- 1 


- 1 




(3) 


26 


36 


45 


78 




- 11 


- 11 


- 11 


- 11 


(4) 


42 


58 


63 






- 12 


- 22 


- 21 




(5) 


46 


79 


87 






- 34 


- 43 


- 40 


etc. 



775. Grade 2A. — Subtraction within the tables. 
Written subtraction, without borrowing; numbers of two 
and three orders. 

99 87 

-78.-62 

899 413 

- 678 - 202 

776. Grade 2B. — Subtraction with borrowing; two 
or three orders. Special attention given to proofs and 
accuracy. 

(1) 426 368 borrowing tens only. 

- 117 - 249 

(2) 426 368 borrowing hundreds and 

- 137 — 276 tens. 



406 METHODS IN EDUCATION 

(3) Use of zero and borrowing. 

804 790 506 300 

— 322 - 648 - 268 — 124 

Methods used in subtraction: borrowing. 

425 
- 186 

6 from 5 I cannot take; borrow 1 ten from the 2 tens, 
add to the 5 units, making 15 units. 8 tens from 1 ten 
I cannot take, so I borrow one 100 (or 10 tens) from 
4 hundreds. 

10 tens and 1 ten =11 tens 
8 from 11 leaves 3 
1 from 3 leaves 2 
239 ans. 

Explanation by decomposition: 

425= 4h. + 2t. + 5u. = 400+ 20+ 5 

= 3 h. + 11 t. + 15 u. = 300 +110+15 

_ 186 = - Ih. + 8t.+ 6u . = 100+ 80+6 

1 h. + 3 t. + 9 u. = 200 + 30 + 9 
Methods in subtraction: the tens method. 

425 
- 186 

6 from 5 I cannot take, so I add 10. 6 from 15 = 9. 

When I add 10 to the minuend, I must add 10 to the 
subtrahend. (Principle of subtraction: If both minuend 
and subtrahend be equally increased, the difference will 
not be changed.) 

9 from 2 I cannot take, so I add 100 to the minuend. 
100 = 10 tens 
9 from 12 = 3. 



ARITHMETIC 407 

According to principle, add 100 to subtrahend. 
, 2 from 4=2 
239 ans. 
Explanation by decomposition: 

425 + 10 + 100 = 4 h. + 12 t. + 15 u. 
- 186 + 10 + 100 = 2h. + 9t. + 6u. 

2 h. + 3 t. + 9 u. = 239 
Methods in subtraction: German or complementary. 

425 

- 186 

I cannot take 6 from 5, so I take 6 from 10 = 4. 

5+4=9 
When you say " from ten " in the units column, add 

1 to the next subtrahend. (No reason given.) 9 from 

2 I cannot take; 9 from 10 = 1; 2 and 1 are 3. Add 
1 to next subtrahend; 2 from 4=2. Ans. 239. 

The advantage of this method is that subtraction 
facts through 10 only need to be learned. 

Methods in subtraction : Austrian or additive. — The 
process of finding what must be added to the subtrahend 
to produce the minuend. 

425 

- 186 

6 and 9 are 15 " 

8 ''3 'Ml first way. 

1 '^ 2 '' 3 . 
Explanation : 

425 = 400 + 20 + 5 = 300 + 110 + 15 
186 = 100 + 80 + 6 = 100+ 80+6 

200+ 30+9 



408 



METHODS IN EDUCATION 



and are 
6+9 = 15' 

9+3=12 second way. 
2+2= 4 J 
Explanation. Add 10 to each, then 100. 
425 = 400 + 20 + 5 = 400 + 120 + 
186 = 100 + 80 + 6 = 200 + 90 + 



15 
6 



200+ 30+ 9 
Advantages. No subtraction tables need be learned. 
Addition facts being used so much more frequently than 
those of subtraction, there is an increase of speed and 
certainty. 

To prove subtraction, add subtrahend and remainder 
to produce minuend. 

777. Grade 3A. — Numbers of four orders. 
7314 8420 

- 3247 - 6548 etc. 



778. Grade 2B. 

tipliers 2, 3, 4, 5. 

Preparation. 

Presentation. 
lowing way: 



Multiplication 
— Multiplicands of two orders; mul- 

Counting by 2's, 3's, 4's, 5's (review). 
Develop multiphcation tables in fol- 



2 

2 2 
2 2 2 


2 
2 
2 
2 


2 
2 
2 
2 
2 etc. 


How many times have I written 1? 

Write 1 times 2=2. 

What is the symbol for times? X . 


1 time. 



ARITHMETIC 409 

Write it on board. 

How many times have I written 2? 2 times. 

2X2=4 etc. 
When you have developed tables, ask children to 
write the work in vertical form. 

2 2 2 2 2 2 

0< 22< 3X fX _5_X 6X etc. 

After tables have been developed and written in ver- 
tieal form, write : 

173 
TO -u 

*11 Children say 2 X 11 = 22. 

2X 
22 
Here is another way of doing it : 

II 

11 2X1 unit = 2 units. 

2 X Put 2 in units place. 
22 2X1 ten= 2 tens. 

Put 2 in tens place. 
Have children notice that product is same. 
Order of difficulties: 

24 23 30 52 

2X 2X 2X 2X 

Multiplication involving carrying. Multipliers 2, 3, 4, 5. 
Preparation. Drill on multiplication tables. 

II 

26 2X6 units = 12 units. 

2X Put down 12. 

12 2X2 tens = 4 tens. 

4 Put 4 in tens place. 

52 Add: 4 tens + 1 ten = 5 tens. 



410 METHODS IN EDUCATION 

Shorter way: 

m 

26 2X6 units = 12 units. 

2 X 12 units = 1 ten and 2 units. 

52 Put 2 in units place. 

2X2 tens = 4 tens. 
4 tens + 1. ten = 5 tens. 
Order of difficulty. Multipliers 2, 4, 5, 3. 
779. Grade 3A. — Multiplication of numbers of three 
orders by numbers of one order. 
Order of difficulty: 

113 124 345 

6X 6X 6X 

104 340 142 

6X 6X 10 X 



780. Grade 3B. — Multiplication of numbers of three 
orders by numbers of two orders. 
Preparation. 

27 27 

3X 10 X Review. 

Presentation. 13 is the same as 1 ten and 3 units. 

g'3 

27 What shall we multiply by first? 

13 X By 3. 



81 3 what? 

270 3 units. 



351 Multiply. 

Now what is the next figure? 
1. 

1 what? 
1 ten. 



ARITHMETIC 411 

Multiply by 10 units. 
270 units. 

What shall I do to get the product? 
Add. 
Why? 

Because we multiplied by 10 and 3, and that is the 
same as multiplying by 13. 
Let us take an easier way. 

Multiply by 3 units. 



fl g fl 

27 Now- what is the next figure? 

13 X 1. 



81 1 what? 

27 Iten. 

351 1 ten X 7 = 

7 tens. 
Where shall I put it? 
In the tens place. 
1 ten X 2 tens (or 20) = 20 tens. 
20 tens = 2 hundreds. 
Put 2 in hundreds place. Add. 
Have children notice that we omitted in units place. 



127 


107 


470 


13 X 


13 X 


26 X 



381 321 2820 

127 107 940 

1651 1391 13220 



412 METHODS IN EDUCATION 







Division 






781. Grade 2B. 


— Short division 


, without remainders. 




Preparation. 




2 


2 

2 


■ 




2 


2 


2 




2 


2 


2 


2 etc. 





How many 2's in 2? 1. 

How many 2's in 4? 2. 

How many 2's in 6? 3. 

How many 2's in 8? 4. 

What is addition sign? +. 

What is subtraction sign? — . 

What is multipUcation sign? X. 

What is division sign? -i- . (If they do not know, 
tell it.) 

Presentation. Read from board, 2-^2. 

W^hat does this mean? It means to separate the first 
number (dividend) into groups of 2's, and tell how many 
there are. It means how many 2's in 2? 4 -v- 2 = ? 
What does this mean? It means to separate 4 into 
groups of 2's, and tell how many 2's in 4, etc., etc. 

I shall show another way to write a division example. 
2J2~ 2)T~ 2JQ~~ 

Read: What does it mean? 
10 12 

2)'20" 2)24 

Then teach inexact division. What does this mean? 

2)5 It means separate 5 into groups of 2's. 



// // / 



How many 2's? 2 2's and 1 remaining. 



ARITHMETIC 413 



2)7 2)9 2)11 2)13. etc. 

782. Grade 3A. — Short division with remainders. 
1 6 How many 2's in 3 tens? 
2) tens units 1 and 1 remaining. 
3 2 1 what? 

1 ten. 
1 ten = 10 units; 10 u. + 2 u. = 12 u.; how many 
2's in 12? 
6 2's in 12. 
Order of difficulty: 



2)452 2)728 2)1608 2)1430 

Divide by 3, 4, 5, 6, 7, 8, 9. 
783. Grade 3B. — Long division. 

1. How many 2's in 4? 2. 
20)40 2. Then how many 20's in 40? 2. 

3. Which number did you try first? 2. 
1. How many 3's in 12? 4. 
4 2. Then how many 30's in 120? 4. 

30)120 3. Which number did you try first? 3. 
1. How many 2's in 17? 8. 

8 2. How many 20's in 170? 8. 

20)170 3. Which number did you try first? 2. 

We call the number we try first the trial divisor. 

Presentation. I shall show you another way of 
writing this example. How many 2's in 17? 

1. How many 20's in 170? 8. 
20)170 2. Multiply 8 X 20 = 160. 

160 = 8X 20 3. How much left? 

10 4. Say nothing about remainder. 



414 METHODS IN EDUCATION 

21 1. Which number do we try first? 



21)441 










42 = 2 X 21 


2. 


How many 2's in 


4? 


2. 


21 


3. 


How many 21's 


in 


44 tens? 


21 = 1 X 21 tens. 











4. 
5. 


Multiply. 
Left? 2 tens. 






6. 2 tens = 20 u. 


20 u. + 1 u. = 21 


u. 




7. How many 2's 


in 2 


. 






8. How many 21 


s in 


21? 






9. Multiply. 










Class tell steps. 










31 




1. Try. 







31)961 2. Divide. 

93 3. Multiply. 

31 4. Compare. 

31 . 5. Subtract. 

First Step. 6. Compare. 

7. Bring down. 

Second Step. When the divisor is contained in one 
or more of partial dividends fewer times than the trial 
divisor is contained in trial dividend. 

43 



35)1505 
140 
105 
105 



Third Step. When the divisor is contained in one < 
or more of partial dividends a greater number of times 
than trial divisor is contained in trial dividend. 



ARITHMETIC 415 

93 



19)1767 
171 

57 
57 

Fourth Step. When a zero occurs in quotient. 

27 

205 



32)6587 
64 

187 
160 

27 

References on this Chapter 

Smith, The Teaching of Mathematics, 1909, Teachers 
College Monograph. 

Smith, The Teaching of Elementary Mathematics, 1900, 
Macmillan. 

Young, The Teaching of Mathematics, 1907, Longmans. 

McLellan and Dewey, The Psychology of Number, 
1908, Applet on. 

McMurry, Special Method in Arithmetic, 1908, Mac- 
millan. 

Jackson, The Educational Significance of Sixteenth 
Century Arithmetic, 1906. 

Conant, The Number Concept, 1896. 

Brooks, Philosophy of Arithmetic, 1902. 

Mary Louise Eastman, The Teaching of Primary 
Arithmetic, in McEvoy Magazine, May, June, Novem- 
ber, and December, 1910, and January, 1911. 



416 METHODS IN EDUCATION 

Annie B. Conselyea, Devices in Arithmetic for Elemen- 
tary Grades, in McEvoy Magazine, December, 1910. 

McNair, Division of Decimals, in McEvoY Magazine, 
January and February, 1911. 

W. A. Cornish, Department of Mathematics, State 
Normal School, Cortland, N. Y., who personally directed 
the revision of the chapter on arithmetic for this edition. 



CHAPTER XVI 
QUESTIONS ON THE TEXT 

I. Comment on the meaning of education as defined 
by Butler. 

' 2. Mention six subjects in an elementary course of 
study and classify each under the intellectual inheritances 
discussed by Butler. 

3. Define and illustrate correlation, co-ordination, 
concentration, and enrichment as applied to a cur- 
riculum. 

4. Explain and apply the culture epoch theory. 

5. Define apperception. Illustrate its application 
in (a) first-year reading, (b) eighth-year arithmetic. 

6. What is meant by a principle of education? Dis- 
tinguish principles of education and maxims of teaching. 

7. Define habit. What are the three fundamental 
laws of habit? 

8. What do you understand by interest in the educa- 
tional use? Show relation of attention and interest. 

9. What is meant by a mental faculty? Mention the 
faculties in their natural order of development. 

10. Show that habit includes all the aims of education. 

II. What are the advantages of opening exercises? 
Prove your answer by showing relation to habit. 

12. What is implied in the term ''group teaching"? 
Advantages? 

13. Outline affirmative and negative arguments on 
home study. 

417 



418 METHODS IN EDUCATION 

14. Discuss examinations in regard to (a) purposes, 
(b) kinds, (c) marking. 

15. Mention five suggestions to guide the moral 
instruction of pupils. 

16. What is punishment? Classify kinds as approved 
and disapproved. 

17. Give three objections to corporal punishment. 
Show bearing of inhibition by repression. 

18. Give favorable and adverse criticisms of the 
Socratic method. Briefly discuss three other methods. 

19. It is said that the inductive process of reasoning 
leads to the general notion. Explain meaning and 
formation of a general notion. In your answer show 
that the general notion utilizes sensation, perception, 
imagination, memory, judgment, and reasoning. 

20. Explain and illustrate (a) apperceiving mass or 
group, (6) reaction in psychology, (c) artificial incentives. 

21. Name five school virtues that should be substi- 
tuted respectively for five school vices, and explain your 
method of inhibiting by substitution. 

22. What is your interpretation of the term general 
method? Show how it embodies the inductive-deductive 
method, method-whole, from particular to general, and 
from concrete to abstract. What is its relation to the 
apperceptive process? 

23. State three causes of inaccuracy in spelling. 

24. Make a list of ten words frequently misspelled, 
give reasons for difficulty in each word, and state specifi- 
cally how to teach pupils to observe and overcome such 
difficulties. * 

25. How should homonyms be taught? 

26. What uses of the dictionary can be taught in (a) 
primary grades, (6) grammar grades? 



QUESTIONS ON THE TEXT 419 

27. Illustrate a practical way of teaching word- 
analysis by applying it to five words. 

28. Outline five other ways of teaching the meaning 
of words. 

29. (a) What is the meaning of dictation exercises? 
(6) What is the aim or purpose? (c) Describe faulty 
dictation exercises, (d) Illustrate appropriate dictation 
work for an intermediate grade. Make it correlate at 
least four subjects of instruction. 

30. Types are bases of apperception. Explain; illus- 
trate a type in grammar, spelling, geography. 

31. What are three uses of a model in composition? 

32. What is the difference between criticism and 
correction of compositions, from the teacher's point of 
view? 

33. Outline five plans of criticism, and then defend 
a composite plan. 

34. Present a commendable plan of correcting com- 
positions after criticism. 

35. What fundamental facts in grammar may be used 
in helping pupils acquire useful habits of mental activity? 

36. What is the critical distinction between an attri- 
bute adjective and an adverb modifier? 

37. Outline a lesson on adverb modifiers according 
to the Herbartian steps. 

38. Cite the rules governing the use of shall and will. 

39. Classify participles according to use. 

40. Illustrate ten uses of infinitives. 

41. What are the essential facts in a lesson on concord 
of relative pronoun and antecedent? 

42. Justify the statement that the development lesson 
uniting words, phrases, and clauses is in accordance with 
the requirements of apperception. 



420 METHODS IN EDUCATION 

43. Select a definition of geography and defend your 
selection. 

44. Using your home city as a type, you prepare a 
lesson-plan for a primary class. What topical headings 
do you use in your plan? 

45. Outline a lesson on Alaska. What elements of 
prior knowledge can you utilize? Under habituation 
to formal outlines, what topics will a child expect to 
find in your outline? Quote section as authority. 

46. Comparison in geography is a guaranty of mental 
economy. Explain, defend, or disprove. 

47. Select three important subjects for lessons in 
geography, give reasons for your selections, and mention 
points of strength and weakness in the lessons as pre- 
sented in this book. 

48. Express your approval or disapproval, with 
reasons on (a) the suggested way of studying a map, 
(6) the suggested way of studying the text. 

49. State specifically how the teaching of geography 
helps in forming desirable habits for life. 

50. How does instinctive imitation tend to strengthen 
character in primary history work? 

51. Show that history and civics stimulate the spirit 
of patriotism in grammar grades. 

52. Outhne a lesson in history to illustrate cause and 
effect. 

53. Refer to five sections that suggest ways of making 
history real to elementary pupils. 

54. Comment on (a) the use of note books, (b) the 
source method, (d) the means of correlation in teaching 
history and civics. 

55. What conditions determine the selection of read- 
ing-matter in the first year? 



QUESTIONS ON THE TEXT 421 

56. Contrast the old and the new types of books in 
reading. 

57. (a) What four methods are combined in the Mc- 
Closkey method in reading? (b) Do you approve a 
combination method? Why? Is this method analytic- 
synthetic? Why? 

58. Briefly characterize the Aldine method. 

59. What physical and mental difficulties may be 
encountered in teaching reading? 

60. Classify the difficulties found in ordinary selec- 
tions for reading, and tell how each difficulty should be 
removed. 

61. Justify your way of helping pupils memorize a 
selection. 

62. Select five important topics in reading, aside from 
the topics in the seven preceding sections, and give 
reason why each selection is important. 

63. Prove that the habit of intelligent interpretation 
in reading is a source of success in all the other work in 
school. 

64. Tell specifically what you do in teaching counting 
in the first grade. Show application of measuring. 
What would you measure and with what would you 
measure? 

65. Explain the procedure in teaching division of 
decimals. What rule or principle results? 

66. Give, in the order of difficulty, five examples you 
would use in teaching short division. 

67. What is meant by a type in arithmetic? Name 
the five type examples in common fractions and per- 
centage. Give graphic illustration of one of the types 
in fractions; and make a practical, concrete problem to 
illustrate one of the types in percentage. 



422 METHODS IN EDUCATION 

68. Tell how you teach longitude and time in arith- 
metic. Show three direct correlations with life. 

69. Illustrate and explain borrowing and carrying in 
arithmetic. 

70. Enumerate three methods of teaching percentage. 
Make a practical problem and solve it to illustrate the 
three ways just mentioned. 

71. Write analysis of the problem given in answer to 
70. 

72. What is meant by business applications of per- 
centage? Illustrate three such applications by making 
three concrete problems. 

73. Explain and illustrate graphic methods in arith- 
metic. Why do such illustrations help apperception? 

74. Briefly describe five devices in teaching arithmetic. 

75. Define number. Give psychological justifica- 
tion of your definition. 

76. Defend two conceptions of common fractions. 

77. Solve a problem by unitary analysis; explain; 
contrast variable unit process applied to the same 
problem. 

78. Induction, deduction, and analogy are mentioned 
under kinds of reasoning. Illustrate induction by out- 
lining a lesson on division of a common fraction by an 
integer; deduction in division of decimals; analogy in 
history. 

79. Describe three ways of performing subtraction. 
Quote page in this book. Advocate, giving authority, 
your choice of the three ways 

80. Accuracy is a habit classified as a school virtue. 
This habit depends upon knowing how to study. Tell 
explicitly how you teach pupils to acquire accuracy in 
studying (a) spelling, (6) model in composition, (c) a 



QUESTIONS ON THE TEXT 423 

problem in reduction of denominate numbers, {d) a 
selection for memorizing. 

81. Consult section 70 for discussion of reaction. 
There are motor reactions in speaking, singing, writing, 
drawing, dancing, etc. Show how five kinds of motor 
reaction help in fixing impressions. Be specific in your 
answer, e.g., how written expression tends to mastery 
of thought in arithmetic, history, and other subjects. 

82. You aim to develop the critical habit of detection 
and correction of errors, (a) What is your procedure 
in written compositions? (6) Apply to map-sketching 
in history and geography, (c) What plan of checking 
(verifying or proving) do you teach for each of the four 
fundamental operations in arithmetic? 

83. The law of self-activity of the pupil applies at 
all times. State briefly and explicitly how you employ 
this instinct in five different educative ways. 

84. Evils and virtues are treated in sections 166 and 
167. Those virtues become a part of character by a 
process of gradual habituation. For each of those 
virtues, show one way in which your teaching strengthens 
character. 

85. Three laws underlying habit are plasticity, motive, 
regular repetition. Show bearing of these laws on 
teaching primary arithmetic. Mention five kinds of 
drill to secure accuracy and rapidity. 

86. In speaking of training the memory, we have the 
terms apprehension, retention, and reproduction; associa- 
tion by similarity and contiguity. Illustrate the first 
three in teaching The Children's Hour; apply sim- 
ilarity and contiguity in geography, using New York 
City as an illustrative type. 

87. What contemporary events in English history 



424 METHODS IN EDUCATION 

should be studied in connection with the American 
Revolution? Justify your answer by principles of edu- 
cation. 

88. Mention five ways in which methodical daily 
teaching tends to strengthen the power of attention of 
pupils. 

89. Alertness, persistent thinking, and co-operative 
activity are three desirable indications of effectual 
teaching. Discuss questioning, under a limit of two 
hundred words, in relation to these ends. 

90. ''Turn to use " is a maxim in education. Apply 
this maxim by outlining ten ways of enlarging pupils' 
vocabularies in the elementary schools. 

91. What is the connotation of the words originality 
and spontaneity (a) from the teacher's viewpoint in 
management, (b) from the pupil's viewpoint in composi- 
tion? 

92. What is the value of drill in education? Briefly 
present your methods and devices in two subjects. 

93. What is meant by a good school spirit? How is 
it secured? 

94. Education implies mental, moral, and physical 
development. Show how the work of one day in school 
may exemplify the truth of this statement. 

95. Every element in school organization carries an 
opportunity in education. Enumerate ten such oppor- 
tunities, aside from assigned subject-matter. (Think 
of marching, singing, cleaning boards, arranging books 
in desks, etc.) 

96. Mention ten of the teacher's methodical ways 
that are worthy bases for pupils' habits. To what 
extent is imitation operative? Apply suggestion also. 

97. If you are asked to outline a discussion of topics 



QUESTIONS ON THE TEXT 425 

I and II, what other points do you desire to add? If no 
others, state tersely why you think the points given are 
adequate. Would such school habits be good hfe habits? 
I. Securing and retaining attention. 

1. Comfortable environment. 

2. Personality of teacher: attractive appearance, in- 
viting manner, persuasive voice. 

3. Habit of expectancy in pupils in relation to board, 
charts, presentation of lesson, drill, and assignment; i.e., 
variety. 

4. Interest through play-impulse. 

5. Orderly, progressive questions; get pupil to ask 
himself questions. 

II. How to interest pupils. 

1. Teach them how to work: consciousness of power 
to accomplish something. 

2. Sympathy, leadership, recognition of meritorious 
results. 

3. Adaptation through proper grading and grouping; 
discouragement obviated. 

4. Useful methods in teaching: graphic, varied; 
processes worthy of imitation when pupil is studying 
alone. 

98. Define reasoning. Can you prove that pupils 
are learning to reason when they are seeking reasons for 
each of the school virtues? Does the will enter this 
process? 

99. Comment on this conclusion by Rousseau: " Edu- 
cation is certainly nothing but a formation of habits." 

100. Define method. 



INDEX 



146 
74 
18 
74 
46 
93 
85 



36 

40 

43 

101 



References are to Pages. 

For Consecutive Topics, see Table of Contents. 

divisors 356 

elimination of matter . . 389 

factors 357 

fractions, common .... 362 

fractions, decimal 372 

graphic method 350 

Grube method 349 

habits, automatic 336 

history 323 

interest, simple 383 

marking papers 332 

measurement 320, 347 

method 325 

methods in primary- 
number 401-417 

modern view 316 

multiples 360 

multiphcation 342, 408 

multiplication tables, 

order 345 

New York City view ... 392 

number defined 318 

partition 347 

percentage 380 

problems 333, 387, 390 

properties of number . . 351 

quantity 316 

ratio 384 

scoring 327 

series 386 

short processes 384 

Speer method 350 

subtraction 339, 404 

subtraction, four ways . 341 
teaching concept of 

number 327 

text-books 388 



Abstract in composition . 

Adolescence 

.Esthetic inheritance .... 

Affiliated interests 

Air shafts 

Analytic method 

Answers desired 

Apperception 

defined 

law 

principle 

Application, formal step . 

Arithmetic 316-417 

addition 335, 401 

aim 321 

algorism 338 

arithmetical comple- 
ment 387 

association, law 344 

Austrian method of di- 
vision 377 

book, early use 330 

casting out nines 387 

combinations 336 

commutation, law .... 344 

correlation 30 

counting and measuring 320 
decomposition . .337, 339, 342 
denominate numbers . . 379 

devices for drill 330 

difficulties graded . . 396, 399 

distribution, law 344 

divisibility, tests 353 

division 347, 412 



427 



428 



INDEX 



Arithmetic (Continued) 

type examples in frac- 
tions and percentage . 397 

unitary analysis 386 

utility 322 

variable unit 386 

Assimilation 20 

Association, formal step . . . 101 
Attention 

defined 37 

law 40 

principle 43 

Attribute complement, lesson 105 
Authority in moral educa- 
tion 70 

B 

Bailey 366 

Batavia plan 62 

Boyer 39 

Butler 6 

C 

Civics 257-279 

Committee of Fifteen .11, 14, 16 

Committee of Ten 214 

Comparison 

formal step 101 

geography 224 

spelling 119, 134 

Composition 140-159 

aims 140 

classification 143 

criticism 151 

culture 140 

miodel, uses of 148-151 

motives for pupils 141 

pertinent questions an- 
swered 153 

principles 322 

problems 146 

structural errors 152 

subjects 146 

utility 140 

Concentration 13, 14 

Concepts 39 

Conception 39 

Consciousness 36 

Co-operation 70, 138 



Co-ordination 14 

Correlation 

Committee of Fifteen 

quoted 11 

illustrated 10 

in course of study 
10-13, 22, 26 

Course of study 5-15 

and pupils 5 

and teacher 5 

assimilation 20 

Butler 6 

concentration 13, 14 

continuity 22 

co-ordination 14 

correlation. .10, 14, 22, 26-32 

culture epochs 9 

curriculum distin- 
guished 5 

eclectic 7 

enrichment 8 

formal vs. content 

studies 32 

Maxwell quoted . , .7, 15-35 

objectivity 21 

old and new 7 

principles 6, 15 

variety 20 

Curriculum 5 

D 

Decoration of rooms 47 

Deductive method 92 

Demerit marks 72 

Device 

arithmetic 330 

geography 229 

management 75 

meaning 98 

word-building 133 

Dexter and Garlick .... 36, 37, 39 
Dictation 

abuse in spelling 114 

composition 145 

spelling 135 

Discipline 70 

Discussion 95 

class 95 

school management ... 50 



INDEX 



429 



Doors and windows 46 

Drawing 

sesthetic 18 

correlation 31 

Drill, formal step 101 

Dutton 46, 47 

E 

Education 

affiliated interests .... 74 

and environment 16 

habit a result 40 

inheritances 6 

^oral 65 

object 16 

principles 35-45 

purpose 3 

Elaboration in composition . 146 

Enrichment 8 

Evils, school 74 

Examinations 128 

Expulsion 72 

F 

Faculties 

defined 36 

object or action 36 

training 40 

Fatigue 75 

Feeling 

defined .' 36 

habit 40 

Fireplace in ventilation .... 47 

Formal instruction 32 

Formal steps of instruction . 100 

G 

Garlick 48 

General method 98-101 

aim 102 

formal steps 100 

Herbartian view 99 

Hervey cited 103 

illustration 105 

method- whole 108 

Generalization, formal step . 101 

Geography 201-257 

causal relations and 

series 219 



climate 235 

commercial trips 231 

Committee of Ten 

quoted 214 

comparison 224 

compass, points of .... 209 

concentric circles 217 

correlation 30 

debates 231 

definitions 202 

devices 229 

early lessons 208 

excursions 213 

glaciers 240 

globe 232 

home geography 208 

how to study 225 

how to study map 252 

how to study text 254 

icebergs 242 

international date line . 247 

latitude and longitude . 245 

man and nature 219 

maps 209, 229 

methods 211 

models 219 

moisture, forms of .... 237 

new way 202 

New York City view . . 203 

old way 201 

pictures 227 

rain 238 

recitation 226 

seasons 242 

shape of earth 233 

standard time 248 

text-books, character- 
istics 256 

volcanoes 248 

winds 250 

Gordy 37, 109 

Grading 58 

Grammar 159-201 

adjective and adverb 

distinguished 171 

adjective clauses 189 

analysis 165 

attribute complement, 

lesson on 105 



430 



INDEX 



Grammar (Continued) 

connectives 194 

diagrams 165 

drill 166 

false syntax 168, 198 

fundamental facts .... 161 

habit 160 

infinitives 178, 186 

mode 176 

noun, lesson on 176 

noun clause, lesson on . 191 

parsing literature .... 167 

participles 178 

parts of speech 169 

personal and relative 

pronouns 173 

shall and will 174 

syllogism 161 

value 159 

words, phrases, clauses 188 

Grounds, uses of 48 

Group teaching 60 

H 

Habit 

and program 54 

defined 39 

habituation 40 

result in education .... 40 

Halleck 36,38 

Harmony with environment 16 

Harris 322, 323, 325, 334 

Heeter 220 

Hervey on formal steps .... 103 

Hill 323, 325 

History 257-279 

cause and effect 269 

collateral reading 268 

correlation 30, 271 

definition 260 

institutional 19, 257 

interest 276 

maps 273 

means of enlivening . . . 274 

memorizing 270 

method 263 

mistakes in teaching . . 277 
New York City view . 257-260 

note books 273 



outlines 273 

reviews 271 

source method 267 

teacher's preparation . . 264 

text-book method 267 

topical method 266 

value 261 

Home lessons 64 

Home 37, 39 

How to study 

geography 228, 252, 255 

grammar 160 

opening exercises 54 

selection for memoriz- 
ing 208 

spelling 112 

value of program 54 

I 

Imagination 

constructive in geog- 
raphy 211 

defined 39 

in moral education .... 69 

Incentives 73 

Inductive method 91 

Institutional inheritance ... 19 

Intellectual inheritances ... 18 
Interest 

defined 36 

law 40 

principle 43 

J 

James on reaction 43 

Judgment 

defined 39 

faculty 40 

training 40 

K 

Knowing defined 36 

L 

Language work correlated . . 31 

Light 45 

Literary inheritance 18 

Logical unity 23 



INDEX 



431 



M 

Maxwell 

courses of study. . . .7, 15-35 

geography 228 

group teaching 60 

oral composition 143 

principles of manage- 
ment 50 

McLellan and Dewey 

318, 319, 321, 348, 350, 365 

McMurry 

arithmetic 322 

^ geography 214, 221 

Memory defined 39 

Memory gems 

correlation 32 

for opening exercises . . 55 

our platform 57 

reading 311 

Method 

defined 76 

general 98-110 

Methods of teaching 76-98 

analytic 93 

analytic and synthetic 

distinguished 94 

concrete to abstract ... 88 

conversational 77 

deductive 92 

development 77 

heuristic 90 

inductive 91 

inductive-deductive ... 92 
known to related un- 
known 88 

lecture 78 

observation before rea- 
soning 89 

particular to general ... 86 

Prussian 91 

questioning 78 

simple to complex 87 

Socratic 82 

synthetic 93 

text-book 96 

topical 95 

Method-whole 108 

Mind 

defined 36 



faculties 40 

training 40 

Monroe , 76 

Moral education 65 

Multiple sense instruction . 245 

O 

Object teaching 35 

Observation defined 38 

Opening exercises 54 

Our platform 57 

Outlines 

composition 150 

geography 228 

history 273 

P 

Paraphrase in composition . 145 

Parker 207 

Pedagogics 4 

Penalties 72 

Percept 38 

Personality 53, 65 

Preparation, formal step ... 100 

Presentation, formal step . . 100 
Principles 

character 66 

composition 141 

course of study 21 

education 41 

management 50 

mind training 40 

moral education 69 

reading 281 

Principles of education . . . .35-45 

Program, value of 53 

Promotion 58 

Prussian method 91 

Punishment 71 

Q 

Questions 78 

answers desired 85 

consecutive 79 

development 80 

negative rules 81 

positive rules 80 

promiscuous 79 

Socratic 82 



432 



INDEX 



R 

Reaction 

meaning 42 

motor 42 

principle 42 

Reading 279-316 

accent 301 

Aldine method 290 

analytic methods 282 

analytic-synthetic 

methods 284 

appreciative 299 

articulation 301 

biography 308 

complete works 280 

defined 296 

difficulties, mental and 

physical 296 

difficulties remedied . . . 298 

dramatization 285 

eclectic tendency 294 

emphasis 301 

extensive and intensive 305 

former books 279 

home 307 

inflection 302 

interest aroused 297 

interpretative 299 

literature 307 

McCloskey method ... 287 
memorizing . . . .300, 308, 311 

memory gems 311 

modulation 303 

pauses 305 

pitch 303 

principle 281 

reading to pupils 297 

silent 300 

synthetic methods .... 283 
tone, quantity, and 

quality 303 

types, modern 281 

value 279 

Ward method 289 

Reasoning 

defined 39 

faculty 40 

Rein on aim 102 



Religious inheritance 19 

Reproduction in composi- 
tion 145 

Reverence 17, 65 

Roark 9, 38 

S 

School economy 44-50 

School management 50-76 

Scientific inheritance 19 

Seating 47 

Self-activity 

defined 39 

law 40 

principle 44 

Self-government 67, 73 

Sensation defined 38 

Sense-perception 

defined 38 

principle 42 

Smith, D. E. . .319, 322, 324, 325 

334, 341, 350, 374, 377, 391 

Socratic method 82 

Space for each child 45 

SpelUng 110 

books vs. lists 116 

classification of words . 123 
correlation through dic- 
tation . 135 

devices in word-build- 
ing 133 

dictionary, use of 133 

difficulties Ill 

experiments 120 

grouping 134 

how to study 118 

how to teach meaning 

of words 130 

how to teach synonyms . 124 

psychology HO 

rules 122 

three ways of teaching . 117 

value 110 

Spirit of school 66, 74 

Studies, moral values 67 

Substitution 33 

Synonyms, lesson on 124 

Synthetic method 93 



INDEX 



433 



T 

Teacher 

ability to teach 52 

control of class 53 

free discussion 50 

Maxwell on estimating . 52 

. originality 51 

personality 53 

qualifications 52 

responsibility 5Q 

spontaneity 51 

using suggestion 54 

Teaching 

Batavia plan 62 

class , 59 

examinations 62 

group 59 

home lessons 64 

individual 59, 61 

moral 65 

Topical method 95 

Transcription 144 



Type 

examples 397 

course of study 15 

geography 221 

grammar 164, 169 

reading 281 

V 

Variety 20, 22, 33, 136 

Ventilation 47 

fireplace 47 

indirect method 46 

Virtues, school 74 

W 

Welch 37, 38, 39 

Will defined 36 

Willing defined 36 

Words classified 123 

Y 

Young 322,385 



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